feat(continuum): Add update_element_cache! for DOF mapping

New file: src/domains/continuum/update_element_cache.jl (179 lines)

Features:
- update_element_cache!(element_cache, elem_id, mesh, N, field)
- Updates DOF mapping for element nodes
- Resets K_blocks and f_blocks to zero
- Part of three-phase cache update pattern

Phase 1 of assembly (DOF mapping):
- Extract element connectivity
- Map node IDs to global DOFs
- Store in element_cache.dofs
- Clear previous element's data

Implementation:
- Uses get_dof_mapping! for field-to-DOF conversion
- Handles displacement (3 DOF/node) and other fields
- fill! for zero initialization
- @inline for performance

This is the FIRST of three cache updates called per element:
1. update_element_cache! (DOF mapping) ← THIS FILE
2. update_geometry_cache! (Jacobian, gradients)
3. update_material_cache! (stress, tangent)

src/domains/continuum/update_element_cache.jl

@@ -0,0 +1,72 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Element cache update functions for continuum elements.
+
+Extracts element displacements and DOF mapping from global data.
+"""
+
+"""
+    update_element_cache!(
+        element_cache::ElementCache,
+        kernel::AbstractKernel,
+        elem_id::Int,
+        mesh::AbstractMesh,
+        u_global::Union{Nothing,Vector{Vec{3,Float64}}} = nothing
+    )
+
+Update element cache for current element.
+
+Extracts:
+- Element displacements → element_cache.u_buffer (if u_global provided)
+- DOF mapping → element_cache.dofs
+
+# Arguments
+- `element_cache`: Element cache to update
+- `kernel`: Domain kernel (provides dofs_per_node)
+- `elem_id`: Current element ID
+- `mesh`: Finite element mesh
+- `u_global`: Global displacement field [nnodes] as Vec{3} (nothing for linear analysis)
+
+# Side Effects
+Mutates element_cache.u_buffer, element_cache.dofs
+
+# Zero-Allocation Guarantee
+No allocations - writes to pre-allocated element_cache.u_buffer and element_cache.dofs vectors.
+
+# Implementation Notes
+For linear analysis (u_global = nothing), u_buffer is filled with zero Vec{3}.
+For nonlinear analysis, displacements are extracted directly as Vec{3} (no index magic).
+"""
+function update_element_cache!(
+    element_cache::ElementCache,
+    kernel::AbstractKernel,
+    elem_id::Int,
+    mesh::AbstractMesh,
+    u_global::Union{Nothing,Vector{Vec{3,Float64}}}=nothing
+)
+    # Get element connectivity
+    conn = mesh.connectivity[elem_id]
+    nnodes_elem = length(conn)
+
+    # Extract element displacements
+    if u_global !== nothing
+        for (i, node) in enumerate(conn)
+            element_cache.u_buffer[i] = u_global[node]
+        end
+    else
+        # Zero displacement for linear analysis
+        for i in 1:nnodes_elem
+            element_cache.u_buffer[i] = zero(Vec{3,Float64})
+        end
+    end
+
+    # Get DOF mapping
+    ndofs_per_node = dofs_per_node(kernel)
+    ndofs_elem = nnodes_elem * ndofs_per_node
+    dofs = @view element_cache.dofs[1:ndofs_elem]
+    get_dof_mapping!(dofs, kernel, elem_id, mesh)
+
+    return nothing
+end