From 5248f6e4703316606100955f13a1c5e623994b38 Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Sat, 15 Nov 2025 02:18:27 +0200
Subject: [PATCH] chore(basis): Regenerate Lagrange basis functions (remove old
 API)

Regenerate src/basis/lagrange_generated.jl with updated generator.

Changes:
- Remove deprecated eval_basis!() and eval_dbasis!() functions (OLD API)
- Keep NEW API: get_basis_functions() and get_basis_derivatives()
- Add node count to element comments (e.g., "Seg2, 2 nodes")
- Update generation timestamp: 2025-11-13 02:42:16

This is auto-generated code from src/basis/lagrange_generator.jl.
The old API functions are no longer needed as all code now uses
the NEW API (Topology + Basis separation).

Generated: 594 line changes across all 15 Lagrange element types
(Seg2, Seg3, Tri3, Tri6, Tri7, Quad4, Quad8, Quad9, Tet4, Tet10,
Hex8, Hex20, Hex27, Wedge6, Wedge15).
---
 src/basis/lagrange_generated.jl | 342 +++++---------------------------
 1 file changed, 51 insertions(+), 291 deletions(-)

diff --git a/src/basis/lagrange_generated.jl b/src/basis/lagrange_generated.jl
index c107df1..4f81c95 100644
--- a/src/basis/lagrange_generated.jl
+++ b/src/basis/lagrange_generated.jl
@@ -20,7 +20,7 @@
 # Generator:
 #   src/basis/lagrange_generator.jl (symbolic engine)
 #
-# Generated: 2025-11-10 11:31:12
+# Generated: 2025-11-13 02:42:16
 # ============================================================================
 
 # This file generates methods for Lagrange{T,P} where:
@@ -31,7 +31,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Segment, 1}: 2-node linear segment element
-# (Old name: Seg2)
+# (Old name: Seg2, 2 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Segment, 1}})
@@ -40,22 +40,6 @@
         function get_reference_element_coordinates(::Lagrange{Segment, 1})
                         return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Segment, 1}}, ::Type{T}, xi::Vec) where T
-                                    (u,) = xi
-                         @inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
-        end
-         @inline function eval_basis!(::Lagrange{Segment, 1}, ::Type{T}, xi::Vec) where T
-                                    (u,) = xi
-                         @inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Segment, 1}}, xi::Vec)
-                                    (u,) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Segment, 1}, xi::Vec)
-                                    (u,) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
-        end
          @inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 1}}, xi::Vec)
                                     (u,) = xi
                          @inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
@@ -75,7 +59,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Segment, 2}: 3-node quadratic segment element
-# (Old name: Seg3)
+# (Old name: Seg3, 3 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Segment, 2}})
@@ -84,22 +68,6 @@
         function get_reference_element_coordinates(::Lagrange{Segment, 2})
                         return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)), Vec{1, Float64}(tuple(0.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Segment, 2}}, ::Type{T}, xi::Vec) where T
-                                    (u,) = xi
-                         @inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
-        end
-         @inline function eval_basis!(::Lagrange{Segment, 2}, ::Type{T}, xi::Vec) where T
-                                    (u,) = xi
-                         @inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Segment, 2}}, xi::Vec)
-                                    (u,) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1))))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Segment, 2}, xi::Vec)
-                                    (u,) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1))))))
-        end
          @inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 2}}, xi::Vec)
                                     (u,) = xi
                          @inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
@@ -119,7 +87,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Triangle, 1}: 3-node linear triangular element
-# (Old name: Tri3)
+# (Old name: Tri3, 3 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Triangle, 1}})
@@ -128,22 +96,6 @@
         function get_reference_element_coordinates(::Lagrange{Triangle, 1})
                         return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Triangle, 1}}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (1 + -1.0u + -1.0v, +u, +v)
-        end
-         @inline function eval_basis!(::Lagrange{Triangle, 1}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (1 + -1.0u + -1.0v, +u, +v)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Triangle, 1}}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Triangle, 1}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
-        end
          @inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 1}}, xi::Vec)
                                     (u, v) = xi
                          @inbounds return (1 + -1.0u + -1.0v, +u, +v)
@@ -163,7 +115,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Triangle, 2}: 6-node quadratic triangular element
-# (Old name: Tri6)
+# (Old name: Tri6, 6 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Triangle, 2}})
@@ -172,22 +124,6 @@
         function get_reference_element_coordinates(::Lagrange{Triangle, 2})
                         return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(0.5, 0.0)), Vec{2, Float64}(tuple(0.5, 0.5)), Vec{2, Float64}(tuple(0.0, 0.5)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Triangle, 2}}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (1 + -3.0u + -3.0v + 2.0 * u ^ 2 + 4.0 * (u * v) + 2.0 * v ^ 2, -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v), +(4.0 * (u * v)), 4.0v + -4.0 * (u * v) + -4.0 * v ^ 2)
-        end
-         @inline function eval_basis!(::Lagrange{Triangle, 2}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (1 + -3.0u + -3.0v + 2.0 * u ^ 2 + 4.0 * (u * v) + 2.0 * v ^ 2, -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v), +(4.0 * (u * v)), 4.0v + -4.0 * (u * v) + -4.0 * v ^ 2)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Triangle, 2}}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v, -3.0 + 4.0u + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v, -4.0u))), Vec(float.(tuple(4.0v, 4.0u))), Vec(float.(tuple(-4.0v, 4.0 + -4.0u + -4.0 * (2 * v ^ (2 - 1))))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Triangle, 2}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v, -3.0 + 4.0u + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v, -4.0u))), Vec(float.(tuple(4.0v, 4.0u))), Vec(float.(tuple(-4.0v, 4.0 + -4.0u + -4.0 * (2 * v ^ (2 - 1))))))
-        end
          @inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 2}}, xi::Vec)
                                     (u, v) = xi
                          @inbounds return (1 + -3.0u + -3.0v + 2.0 * u ^ 2 + 4.0 * (u * v) + 2.0 * v ^ 2, -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v), +(4.0 * (u * v)), 4.0v + -4.0 * (u * v) + -4.0 * v ^ 2)
@@ -207,7 +143,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 1}: 4-node bilinear quadrilateral element
-# (Old name: Quad4)
+# (Old name: Quad4, 4 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 1}})
@@ -216,22 +152,6 @@
         function get_reference_element_coordinates(::Lagrange{Quadrilateral, 1})
                         return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Quadrilateral, 1}}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (0.25 + -0.25u + -0.25v + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25 * (u * v))
-        end
-         @inline function eval_basis!(::Lagrange{Quadrilateral, 1}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (0.25 + -0.25u + -0.25v + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25 * (u * v))
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Quadrilateral, 1}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u))))
-        end
          @inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
                                     (u, v) = xi
                          @inbounds return (0.25 + -0.25u + -0.25v + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25 * (u * v))
@@ -251,7 +171,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 2}: 8-node serendipity quadrilateral element
-# (Old name: Quad8)
+# (Old name: Quad8, 8 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 2}})
@@ -260,22 +180,6 @@
         function get_reference_element_coordinates(::Lagrange{Quadrilateral, 2})
                         return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Quadrilateral, 2}}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (-0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), 0.5 + -0.5v + -0.5 * u ^ 2 + 0.5 * (u ^ 2 * v), 0.5 + 0.5u + -0.5 * v ^ 2 + -0.5 * (u * v ^ 2), 0.5 + 0.5v + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * v), 0.5 + -0.5u + -0.5 * v ^ 2 + 0.5 * (u * v ^ 2))
-        end
-         @inline function eval_basis!(::Lagrange{Quadrilateral, 2}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (-0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), 0.5 + -0.5v + -0.5 * u ^ 2 + 0.5 * (u ^ 2 * v), 0.5 + 0.5u + -0.5 * v ^ 2 + -0.5 * (u * v ^ 2), 0.5 + 0.5v + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * v), 0.5 + -0.5u + -0.5 * v ^ 2 + 0.5 * (u * v ^ 2))
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + 0.5 * ((2 * u ^ (2 - 1)) * v), -0.5 + 0.5 * u ^ 2))), Vec(float.(tuple(0.5 + -0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + -0.5 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + -0.5 * ((2 * u ^ (2 - 1)) * v), 0.5 + -0.5 * u ^ 2))), Vec(float.(tuple(-0.5 + 0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + 0.5 * (u * (2 * v ^ (2 - 1)))))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Quadrilateral, 2}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + 0.5 * ((2 * u ^ (2 - 1)) * v), -0.5 + 0.5 * u ^ 2))), Vec(float.(tuple(0.5 + -0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + -0.5 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + -0.5 * ((2 * u ^ (2 - 1)) * v), 0.5 + -0.5 * u ^ 2))), Vec(float.(tuple(-0.5 + 0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + 0.5 * (u * (2 * v ^ (2 - 1)))))))
-        end
          @inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
                                     (u, v) = xi
                          @inbounds return (-0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), 0.5 + -0.5v + -0.5 * u ^ 2 + 0.5 * (u ^ 2 * v), 0.5 + 0.5u + -0.5 * v ^ 2 + -0.5 * (u * v ^ 2), 0.5 + 0.5v + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * v), 0.5 + -0.5u + -0.5 * v ^ 2 + 0.5 * (u * v ^ 2))
@@ -295,7 +199,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 2}: 9-node biquadratic quadrilateral element
-# (Old name: Quad9)
+# (Old name: Quad9, 9 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 2}})
@@ -304,22 +208,6 @@
         function get_reference_element_coordinates(::Lagrange{Quadrilateral, 2})
                         return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 0.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Quadrilateral, 2}}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + u ^ 2 * v ^ 2)
-        end
-         @inline function eval_basis!(::Lagrange{Quadrilateral, 2}, ::Type{T}, xi::Vec) where T
-                                    (u, v) = xi
-                         @inbounds return (0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + u ^ 2 * v ^ 2)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2, -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1))))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Quadrilateral, 2}, xi::Vec)
-                                    (u, v) = xi
-                         @inbounds return (Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2, -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1))))))
-        end
          @inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
                                     (u, v) = xi
                          @inbounds return (0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + u ^ 2 * v ^ 2)
@@ -338,228 +226,148 @@
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
-# Lagrange{Tetrahedron, 1}: 4-node linear tetrahedral element
-# (Old name: Tet4)
+# Lagrange{Tetrahedron{4}, 1}: 4-node linear tetrahedral element
+# (Old name: Tet4, 4 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
-    function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron, 1}})
+    function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron{4}, 1}})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
     end
-        function get_reference_element_coordinates(::Lagrange{Tetrahedron, 1})
+        function get_reference_element_coordinates(::Lagrange{Tetrahedron{4}, 1})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Tetrahedron, 1}}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Type{Tetrahedron{4}}, ::Type{Lagrange{Tetrahedron{4}, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
         end
-         @inline function eval_basis!(::Lagrange{Tetrahedron, 1}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Tetrahedron{4}, ::Lagrange{Tetrahedron{4}, 1}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
         end
-         @inline function eval_dbasis!(::Type{Lagrange{Tetrahedron, 1}}, xi::Vec)
+         @inline function get_basis_derivatives(::Type{Tetrahedron{4}}, ::Type{Lagrange{Tetrahedron{4}, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
         end
-         @inline function eval_dbasis!(::Lagrange{Tetrahedron, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
-        end
-         @inline function get_basis_functions(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
-        end
-         @inline function get_basis_functions(::Tetrahedron, ::Lagrange{Tetrahedron, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
-        end
-         @inline function get_basis_derivatives(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
-        end
-         @inline function get_basis_derivatives(::Tetrahedron, ::Lagrange{Tetrahedron, 1}, xi::Vec)
+         @inline function get_basis_derivatives(::Tetrahedron{4}, ::Lagrange{Tetrahedron{4}, 1}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
-# Lagrange{Tetrahedron, 2}: 10-node quadratic tetrahedral element
-# (Old name: Tet10)
+# Lagrange{Tetrahedron{10}, 2}: 10-node quadratic tetrahedral element
+# (Old name: Tet10, 10 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
-    function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron, 2}})
+    function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron{10}, 2}})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.5)), Vec{3, Float64}(tuple(0.5, 0.0, 0.5)), Vec{3, Float64}(tuple(0.0, 0.5, 0.5)))
     end
-        function get_reference_element_coordinates(::Lagrange{Tetrahedron, 2})
+        function get_reference_element_coordinates(::Lagrange{Tetrahedron{10}, 2})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.5)), Vec{3, Float64}(tuple(0.5, 0.0, 0.5)), Vec{3, Float64}(tuple(0.0, 0.5, 0.5)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Tetrahedron, 2}}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Type{Tetrahedron{10}}, ::Type{Lagrange{Tetrahedron{10}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
         end
-         @inline function eval_basis!(::Lagrange{Tetrahedron, 2}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Tetrahedron{10}, ::Lagrange{Tetrahedron{10}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
         end
-         @inline function eval_dbasis!(::Type{Lagrange{Tetrahedron, 2}}, xi::Vec)
+         @inline function get_basis_derivatives(::Type{Tetrahedron{10}}, ::Type{Lagrange{Tetrahedron{10}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
         end
-         @inline function eval_dbasis!(::Lagrange{Tetrahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
-        end
-         @inline function get_basis_functions(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
-        end
-         @inline function get_basis_functions(::Tetrahedron, ::Lagrange{Tetrahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
-        end
-         @inline function get_basis_derivatives(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
-        end
-         @inline function get_basis_derivatives(::Tetrahedron, ::Lagrange{Tetrahedron, 2}, xi::Vec)
+         @inline function get_basis_derivatives(::Tetrahedron{10}, ::Lagrange{Tetrahedron{10}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
-# Lagrange{Hexahedron, 1}: 8-node trilinear hexahedral element
-# (Old name: Hex8)
+# Lagrange{Hexahedron{8}, 1}: 8-node trilinear hexahedral element
+# (Old name: Hex8, 8 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
-    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron, 1}})
+    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{8}, 1}})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)))
     end
-        function get_reference_element_coordinates(::Lagrange{Hexahedron, 1})
+        function get_reference_element_coordinates(::Lagrange{Hexahedron{8}, 1})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Hexahedron, 1}}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Type{Hexahedron{8}}, ::Type{Lagrange{Hexahedron{8}, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
         end
-         @inline function eval_basis!(::Lagrange{Hexahedron, 1}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Hexahedron{8}, ::Lagrange{Hexahedron{8}, 1}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
         end
-         @inline function eval_dbasis!(::Type{Lagrange{Hexahedron, 1}}, xi::Vec)
+         @inline function get_basis_derivatives(::Type{Hexahedron{8}}, ::Type{Lagrange{Hexahedron{8}, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
         end
-         @inline function eval_dbasis!(::Lagrange{Hexahedron, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
-        end
-         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
-        end
-         @inline function get_basis_functions(::Hexahedron, ::Lagrange{Hexahedron, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
-        end
-         @inline function get_basis_derivatives(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
-        end
-         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 1}, xi::Vec)
+         @inline function get_basis_derivatives(::Hexahedron{8}, ::Lagrange{Hexahedron{8}, 1}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
-# Lagrange{Hexahedron, 2}: 20-node serendipity hexahedral element
-# (Old name: Hex20)
+# Lagrange{Hexahedron{20}, 2}: 20-node serendipity hexahedral element
+# (Old name: Hex20, 20 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
-    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron, 2}})
+    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{20}, 2}})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)))
     end
-        function get_reference_element_coordinates(::Lagrange{Hexahedron, 2})
+        function get_reference_element_coordinates(::Lagrange{Hexahedron{20}, 2})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Hexahedron, 2}}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Type{Hexahedron{20}}, ::Type{Lagrange{Hexahedron{20}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
         end
-         @inline function eval_basis!(::Lagrange{Hexahedron, 2}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Hexahedron{20}, ::Lagrange{Hexahedron{20}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
         end
-         @inline function eval_dbasis!(::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+         @inline function get_basis_derivatives(::Type{Hexahedron{20}}, ::Type{Lagrange{Hexahedron{20}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
         end
-         @inline function eval_dbasis!(::Lagrange{Hexahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
-        end
-         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
-        end
-         @inline function get_basis_functions(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
-        end
-         @inline function get_basis_derivatives(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
-        end
-         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+         @inline function get_basis_derivatives(::Hexahedron{20}, ::Lagrange{Hexahedron{20}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
-# Lagrange{Hexahedron, 2}: 27-node triquadratic hexahedral element
-# (Old name: Hex27)
+# Lagrange{Hexahedron{27}, 2}: 27-node triquadratic hexahedral element
+# (Old name: Hex27, 27 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
-    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron, 2}})
+    function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{27}, 2}})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)))
     end
-        function get_reference_element_coordinates(::Lagrange{Hexahedron, 2})
+        function get_reference_element_coordinates(::Lagrange{Hexahedron{27}, 2})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Hexahedron, 2}}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Type{Hexahedron{27}}, ::Type{Lagrange{Hexahedron{27}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
         end
-         @inline function eval_basis!(::Lagrange{Hexahedron, 2}, ::Type{T}, xi::Vec) where T
+         @inline function get_basis_functions(::Hexahedron{27}, ::Lagrange{Hexahedron{27}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
         end
-         @inline function eval_dbasis!(::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+         @inline function get_basis_derivatives(::Type{Hexahedron{27}}, ::Type{Lagrange{Hexahedron{27}, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
         end
-         @inline function eval_dbasis!(::Lagrange{Hexahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
-        end
-         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
-        end
-         @inline function get_basis_functions(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
-        end
-         @inline function get_basis_derivatives(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
-        end
-         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+         @inline function get_basis_derivatives(::Hexahedron{27}, ::Lagrange{Hexahedron{27}, 2}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
         end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Pyramid, 1}: 5-node linear pyramid element
-# (Old name: Pyr5)
+# (Old name: Pyr5, 5 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Pyramid, 1}})
@@ -568,22 +376,6 @@
         function get_reference_element_coordinates(::Lagrange{Pyramid, 1})
                         return (Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Pyramid, 1}}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (0.25 + -0.25u + -0.25v + -0.25w + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25w + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + -0.25w + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25w + -0.25 * (u * v), +w)
-        end
-         @inline function eval_basis!(::Lagrange{Pyramid, 1}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (0.25 + -0.25u + -0.25v + -0.25w + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25w + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + -0.25w + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25w + -0.25 * (u * v), +w)
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Pyramid, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u, -0.25))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u, -0.25))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u, -0.25))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u, -0.25))), Vec(float.(tuple(0, 0, 1))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Pyramid, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u, -0.25))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u, -0.25))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u, -0.25))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u, -0.25))), Vec(float.(tuple(0, 0, 1))))
-        end
          @inline function get_basis_functions(::Type{Pyramid}, ::Type{Lagrange{Pyramid, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (0.25 + -0.25u + -0.25v + -0.25w + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25w + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + -0.25w + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25w + -0.25 * (u * v), +w)
@@ -603,7 +395,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Wedge, 1}: 6-node linear wedge element (triangular prism)
-# (Old name: Wedge6)
+# (Old name: Wedge6, 6 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Wedge, 1}})
@@ -612,22 +404,6 @@
         function get_reference_element_coordinates(::Lagrange{Wedge, 1})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Wedge, 1}}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (0.5 + -0.5u + -0.5v + -0.5w + 0.5 * (u * w) + 0.5 * (v * w), 0.5u + -0.5 * (u * w), 0.5v + -0.5 * (v * w), 0.5 + -0.5u + -0.5v + 0.5w + -0.5 * (u * w) + -0.5 * (v * w), 0.5u + 0.5 * (u * w), 0.5v + 0.5 * (v * w))
-        end
-         @inline function eval_basis!(::Lagrange{Wedge, 1}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (0.5 + -0.5u + -0.5v + -0.5w + 0.5 * (u * w) + 0.5 * (v * w), 0.5u + -0.5 * (u * w), 0.5v + -0.5 * (v * w), 0.5 + -0.5u + -0.5v + 0.5w + -0.5 * (u * w) + -0.5 * (v * w), 0.5u + 0.5 * (u * w), 0.5v + 0.5 * (v * w))
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Wedge, 1}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5 + 0.5w, -0.5 + 0.5w, -0.5 + 0.5u + 0.5v))), Vec(float.(tuple(0.5 + -0.5w, 0, -0.5u))), Vec(float.(tuple(0, 0.5 + -0.5w, -0.5v))), Vec(float.(tuple(-0.5 + -0.5w, -0.5 + -0.5w, 0.5 + -0.5u + -0.5v))), Vec(float.(tuple(0.5 + 0.5w, 0, 0.5u))), Vec(float.(tuple(0, 0.5 + 0.5w, 0.5v))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Wedge, 1}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-0.5 + 0.5w, -0.5 + 0.5w, -0.5 + 0.5u + 0.5v))), Vec(float.(tuple(0.5 + -0.5w, 0, -0.5u))), Vec(float.(tuple(0, 0.5 + -0.5w, -0.5v))), Vec(float.(tuple(-0.5 + -0.5w, -0.5 + -0.5w, 0.5 + -0.5u + -0.5v))), Vec(float.(tuple(0.5 + 0.5w, 0, 0.5u))), Vec(float.(tuple(0, 0.5 + 0.5w, 0.5v))))
-        end
          @inline function get_basis_functions(::Type{Wedge}, ::Type{Lagrange{Wedge, 1}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (0.5 + -0.5u + -0.5v + -0.5w + 0.5 * (u * w) + 0.5 * (v * w), 0.5u + -0.5 * (u * w), 0.5v + -0.5 * (v * w), 0.5 + -0.5u + -0.5v + 0.5w + -0.5 * (u * w) + -0.5 * (v * w), 0.5u + 0.5 * (u * w), 0.5v + 0.5 * (v * w))
@@ -647,7 +423,7 @@
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Wedge, 2}: 15-node quadratic wedge element
-# (Old name: Wedge15)
+# (Old name: Wedge15, 15 nodes)
 # ──────────────────────────────────────────────────────────────────────────────
 
     function get_reference_element_coordinates(::Type{Lagrange{Wedge, 2}})
@@ -656,22 +432,6 @@
         function get_reference_element_coordinates(::Lagrange{Wedge, 2})
                         return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, -1.0)), Vec{3, Float64}(tuple(0.5, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.5, 1.0)), Vec{3, Float64}(tuple(0.0, 0.5, 1.0)))
     end
-         @inline function eval_basis!(::Type{Lagrange{Wedge, 2}}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (-1.0u + -1.0v + -0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + 1.5 * (u * w) + 1.5 * (v * w) + -1.0 * (u ^ 2 * w) + -1.0 * (v ^ 2 * w) + -2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + 0.5 * (u * w) + -1.0 * (u ^ 2 * w) + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + 0.5 * (v * w) + -1.0 * (v ^ 2 * w) + 0.5 * (v * w ^ 2), -1.0u + -1.0v + 0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + -1.5 * (u * w) + -1.5 * (v * w) + u ^ 2 * w + v ^ 2 * w + 2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + -0.5 * (u * w) + u ^ 2 * w + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + -0.5 * (v * w) + v ^ 2 * w + 0.5 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + -2.0 * (u * w) + 2.0 * (u ^ 2 * w) + 2.0 * (u * v * w), 2.0 * (u * v) + -2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + -2.0 * (v * w) + 2.0 * (v ^ 2 * w) + 2.0 * (u * v * w), 1 + -1.0u + -1.0v + -1.0 * w ^ 2 + u * w ^ 2 + v * w ^ 2, u + -1.0 * (u * w ^ 2), v + -1.0 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + 2.0 * (u * w) + -2.0 * (u ^ 2 * w) + -2.0 * (u * v * w), 2.0 * (u * v) + 2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + 2.0 * (v * w) + -2.0 * (v ^ 2 * w) + -2.0 * (u * v * w))
-        end
-         @inline function eval_basis!(::Lagrange{Wedge, 2}, ::Type{T}, xi::Vec) where T
-                                    (u, v, w) = xi
-                         @inbounds return (-1.0u + -1.0v + -0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + 1.5 * (u * w) + 1.5 * (v * w) + -1.0 * (u ^ 2 * w) + -1.0 * (v ^ 2 * w) + -2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + 0.5 * (u * w) + -1.0 * (u ^ 2 * w) + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + 0.5 * (v * w) + -1.0 * (v ^ 2 * w) + 0.5 * (v * w ^ 2), -1.0u + -1.0v + 0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + -1.5 * (u * w) + -1.5 * (v * w) + u ^ 2 * w + v ^ 2 * w + 2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + -0.5 * (u * w) + u ^ 2 * w + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + -0.5 * (v * w) + v ^ 2 * w + 0.5 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + -2.0 * (u * w) + 2.0 * (u ^ 2 * w) + 2.0 * (u * v * w), 2.0 * (u * v) + -2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + -2.0 * (v * w) + 2.0 * (v ^ 2 * w) + 2.0 * (u * v * w), 1 + -1.0u + -1.0v + -1.0 * w ^ 2 + u * w ^ 2 + v * w ^ 2, u + -1.0 * (u * w ^ 2), v + -1.0 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + 2.0 * (u * w) + -2.0 * (u ^ 2 * w) + -2.0 * (u * v * w), 2.0 * (u * v) + 2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + 2.0 * (v * w) + -2.0 * (v ^ 2 * w) + -2.0 * (u * v * w))
-        end
-         @inline function eval_dbasis!(::Type{Lagrange{Wedge, 2}}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + 1.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + 1.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w) + -0.5 * w ^ 2, -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 1.5u + 1.5v + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 0.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0, 0.5u + -1.0 * u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + 0.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0.5v + -1.0 * v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + -1.5w + (2 * u ^ (2 - 1)) * w + 2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + -1.5w + (2 * v ^ (2 - 1)) * w + 2.0 * (u * w) + -0.5 * w ^ 2, 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -1.5u + -1.5v + u ^ 2 + v ^ 2 + 2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + -0.5w + (2 * u ^ (2 - 1)) * w + 0.5 * w ^ 2, 0, -0.5u + u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + -0.5w + (2 * v ^ (2 - 1)) * w + 0.5 * w ^ 2, -0.5v + v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + -2.0w + 2.0 * ((2 * u ^ (2 - 1)) * w) + 2.0 * (v * w), -2.0u + 2.0 * (u * w), -2.0u + 2.0 * u ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(2.0v + -2.0 * (v * w), 2.0u + -2.0 * (u * w), -2.0 * (u * v)))), Vec(float.(tuple(-2.0v + 2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + -2.0w + 2.0 * ((2 * v ^ (2 - 1)) * w) + 2.0 * (u * w), -2.0v + 2.0 * v ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(-1.0 + w ^ 2, -1.0 + w ^ 2, -1.0 * (2 * w ^ (2 - 1)) + u * (2 * w ^ (2 - 1)) + v * (2 * w ^ (2 - 1))))), Vec(float.(tuple(1 + -1.0 * w ^ 2, 0, -1.0 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, 1 + -1.0 * w ^ 2, -1.0 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + 2.0w + -2.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w), -2.0u + -2.0 * (u * w), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v)))), Vec(float.(tuple(2.0v + 2.0 * (v * w), 2.0u + 2.0 * (u * w), 2.0 * (u * v)))), Vec(float.(tuple(-2.0v + -2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + 2.0w + -2.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v)))))
-        end
-         @inline function eval_dbasis!(::Lagrange{Wedge, 2}, xi::Vec)
-                                    (u, v, w) = xi
-                         @inbounds return (Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + 1.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + 1.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w) + -0.5 * w ^ 2, -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 1.5u + 1.5v + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 0.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0, 0.5u + -1.0 * u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + 0.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0.5v + -1.0 * v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + -1.5w + (2 * u ^ (2 - 1)) * w + 2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + -1.5w + (2 * v ^ (2 - 1)) * w + 2.0 * (u * w) + -0.5 * w ^ 2, 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -1.5u + -1.5v + u ^ 2 + v ^ 2 + 2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + -0.5w + (2 * u ^ (2 - 1)) * w + 0.5 * w ^ 2, 0, -0.5u + u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + -0.5w + (2 * v ^ (2 - 1)) * w + 0.5 * w ^ 2, -0.5v + v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + -2.0w + 2.0 * ((2 * u ^ (2 - 1)) * w) + 2.0 * (v * w), -2.0u + 2.0 * (u * w), -2.0u + 2.0 * u ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(2.0v + -2.0 * (v * w), 2.0u + -2.0 * (u * w), -2.0 * (u * v)))), Vec(float.(tuple(-2.0v + 2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + -2.0w + 2.0 * ((2 * v ^ (2 - 1)) * w) + 2.0 * (u * w), -2.0v + 2.0 * v ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(-1.0 + w ^ 2, -1.0 + w ^ 2, -1.0 * (2 * w ^ (2 - 1)) + u * (2 * w ^ (2 - 1)) + v * (2 * w ^ (2 - 1))))), Vec(float.(tuple(1 + -1.0 * w ^ 2, 0, -1.0 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, 1 + -1.0 * w ^ 2, -1.0 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + 2.0w + -2.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w), -2.0u + -2.0 * (u * w), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v)))), Vec(float.(tuple(2.0v + 2.0 * (v * w), 2.0u + 2.0 * (u * w), 2.0 * (u * v)))), Vec(float.(tuple(-2.0v + -2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + 2.0w + -2.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v)))))
-        end
          @inline function get_basis_functions(::Type{Wedge}, ::Type{Lagrange{Wedge, 2}}, xi::Vec)
                                     (u, v, w) = xi
                          @inbounds return (-1.0u + -1.0v + -0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + 1.5 * (u * w) + 1.5 * (v * w) + -1.0 * (u ^ 2 * w) + -1.0 * (v ^ 2 * w) + -2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + 0.5 * (u * w) + -1.0 * (u ^ 2 * w) + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + 0.5 * (v * w) + -1.0 * (v ^ 2 * w) + 0.5 * (v * w ^ 2), -1.0u + -1.0v + 0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + -1.5 * (u * w) + -1.5 * (v * w) + u ^ 2 * w + v ^ 2 * w + 2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + -0.5 * (u * w) + u ^ 2 * w + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + -0.5 * (v * w) + v ^ 2 * w + 0.5 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + -2.0 * (u * w) + 2.0 * (u ^ 2 * w) + 2.0 * (u * v * w), 2.0 * (u * v) + -2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + -2.0 * (v * w) + 2.0 * (v ^ 2 * w) + 2.0 * (u * v * w), 1 + -1.0u + -1.0v + -1.0 * w ^ 2 + u * w ^ 2 + v * w ^ 2, u + -1.0 * (u * w ^ 2), v + -1.0 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + 2.0 * (u * w) + -2.0 * (u ^ 2 * w) + -2.0 * (u * v * w), 2.0 * (u * v) + 2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + 2.0 * (v * w) + -2.0 * (v ^ 2 * w) + -2.0 * (u * v * w))