feat(mesh): Add mesh API with topology ownership and node-to-elements mapping

Create src/mesh/api.jl defining mesh-specific abstractions:
- AbstractMesh base type for all mesh structures
- nnodes_total(), nelements() for mesh sizing
- get_node(node_id) returns Vec{Dim} coordinates
- connectivity_matrix() returns element-to-nodes mapping
- get_elements_for_node(node_id) returns node-to-elements mapping (critical for nodal assembly)
- get_element_set(name), get_node_set(name) for named sets (BCs, materials, postprocessing)
- AbstractRefineStrategy, refine() for adaptive mesh refinement

Meshes own topology (coordinates, connectivity). Multiple Physics can
share one Mesh for multiphysics coupling. Node-to-elements mapping
enables nodal assembly pattern (see docs/book/multigpu_nodal_assembly.md).

Part of systematic modular API architecture.

src/mesh/api.jl

@@ -0,0 +1,233 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Mesh API definitions.
+
+This file defines mesh-specific abstract types and interfaces.
+Must be included after core api.jl.
+"""
+
+# ============================================================================
+# MESH ABSTRACTIONS
+# ============================================================================
+
+"""
+    AbstractMesh
+
+Abstract type for all mesh structures.
+
+# Interface Requirements
+
+Concrete mesh types must implement:
+- `nnodes_total(mesh)` - Total number of nodes
+- `nelements(mesh)` - Total number of elements
+- `get_node(mesh, node_id)` - Get node coordinates
+- `connectivity_matrix(mesh)` - Element connectivity
+- `get_elements_for_node(mesh, node_id)` - Elements containing node
+- `get_element_set(mesh, set_name)` - Get named element set
+- `get_node_set(mesh, set_name)` - Get named node set
+
+# Concrete Types
+- `Mesh{T<:AbstractTopology}` - Parametric mesh with single topology type
+- `MixedMesh` - Mesh with multiple topology types (future)
+
+# Design Philosophy
+
+Meshes own topology (node coordinates, connectivity).
+Physics references meshes (does not own them).
+Multiple Physics can share one Mesh (multiphysics coupling).
+
+# Element Sets and Node Sets
+
+Meshes support named sets for:
+- Applying boundary conditions
+- Defining material regions
+- Post-processing specific regions
+
+# See Also
+- Concrete implementation: `Mesh{T}` in src/mesh/mesh.jl
+"""
+abstract type AbstractMesh end
+
+# ============================================================================
+# MESH OPERATIONS
+# ============================================================================
+
+"""
+    nnodes_total(mesh::AbstractMesh) -> Int
+
+Total number of nodes in the mesh.
+
+# Examples
+```julia
+mesh = Mesh(Tet4(), nodes, connectivity)
+n = nnodes_total(mesh)  # e.g., 1000 nodes
+```
+"""
+function nnodes_total end
+
+"""
+    nelements(mesh::AbstractMesh) -> Int
+
+Total number of elements in the mesh.
+
+# Examples
+```julia
+mesh = Mesh(Hex8(), nodes, connectivity)
+ne = nelements(mesh)  # e.g., 500 elements
+```
+"""
+function nelements end
+
+"""
+    get_node(mesh::AbstractMesh, node_id::Int) -> Vec{Dim}
+
+Get coordinates of a node by its ID.
+
+# Arguments
+- `mesh`: Mesh structure
+- `node_id`: Node identifier (1-based)
+
+# Returns
+- Node coordinates as `Vec{Dim}` (Dim = 1, 2, or 3)
+
+# Examples
+```julia
+X = get_node(mesh, 42)  # Vec{3}(1.0, 2.0, 3.0)
+```
+"""
+function get_node end
+
+"""
+    connectivity_matrix(mesh::AbstractMesh) -> Matrix{Int}
+
+Get element connectivity matrix.
+
+# Returns
+- Matrix where each row is an element's node IDs
+- Size: `(nelements, nnodes_per_element)`
+
+# Examples
+```julia
+conn = connectivity_matrix(mesh)
+elem1_nodes = conn[1, :]  # [1, 2, 3, 4] for Tet4
+```
+"""
+function connectivity_matrix end
+
+"""
+    get_elements_for_node(mesh::AbstractMesh, node_id::Int) -> Vector{Int}
+
+Get all elements containing a given node.
+
+Critical for nodal assembly (node-to-elements map).
+
+# Arguments
+- `mesh`: Mesh structure
+- `node_id`: Node identifier
+
+# Returns
+- Vector of element IDs containing this node
+
+# Examples
+```julia
+elems = get_elements_for_node(mesh, 10)  # [5, 6, 7, 8, 12, 15]
+```
+
+# See Also
+- Nodal assembly: docs/book/multigpu_nodal_assembly.md
+"""
+function get_elements_for_node end
+
+"""
+    get_element_set(mesh::AbstractMesh, set_name::String) -> Vector{Int}
+
+Get element IDs in a named element set.
+
+# Arguments
+- `mesh`: Mesh structure
+- `set_name`: Name of element set (e.g., "body", "surface1")
+
+# Returns
+- Vector of element IDs in the set
+
+# Examples
+```julia
+body_elements = get_element_set(mesh, "body")
+surface_elements = get_element_set(mesh, "traction_surface")
+```
+
+# See Also
+- [`get_node_set`](@ref) for node sets
+"""
+function get_element_set end
+
+"""
+    get_node_set(mesh::AbstractMesh, set_name::String) -> Vector{Int}
+
+Get node IDs in a named node set.
+
+# Arguments
+- `mesh`: Mesh structure
+- `set_name`: Name of node set (e.g., "fixed_nodes", "boundary")
+
+# Returns
+- Vector of node IDs in the set
+
+# Examples
+```julia
+fixed_nodes = get_node_set(mesh, "fixed_support")
+loaded_nodes = get_node_set(mesh, "load_application")
+```
+
+# See Also
+- [`get_element_set`](@ref) for element sets
+"""
+function get_node_set end
+
+# ============================================================================
+# MESH REFINEMENT
+# ============================================================================
+
+"""
+    AbstractRefineStrategy
+
+Abstract type for mesh refinement strategies.
+
+# Concrete Strategies
+- `LongestEdgeBisection`: Recursive longest edge bisection
+- `RedGreenRefinement`: Red-green triangulation
+- `Uniform`: Uniform refinement (split all elements)
+
+# See Also
+- [`refine`](@ref) for refinement function
+- Implementation: src/mesh/refine.jl
+"""
+abstract type AbstractRefineStrategy end
+
+"""
+    refine(mesh::AbstractMesh, strategy::AbstractRefineStrategy) -> AbstractMesh
+
+Refine a mesh using a refinement strategy.
+
+# Arguments
+- `mesh`: Original mesh
+- `strategy`: Refinement strategy
+
+# Returns
+- Refined mesh (new instance)
+
+# Examples
+```julia
+# Longest edge bisection
+refined = refine(mesh, LongestEdgeBisection())
+
+# Uniform refinement
+refined = refine(mesh, Uniform())
+```
+
+# See Also
+- [`AbstractRefineStrategy`](@ref) for available strategies
+"""
+function refine end