Compute P2 (Quadratic) FEM Matrices

Computes finite element matrices using 6-node quadratic triangular elements. Each triangle edge gets a midpoint node, giving 6 basis functions per triangle instead of 3. Quadratic elements provide better approximation accuracy with fewer mesh nodes.

Usage

fem_matrices_p2(mesh)

Arguments

mesh

A tulpa_mesh object (2D only).

Value

A list with:

• C: consistent mass matrix (n_total x n_total sparse)

• G: stiffness matrix (n_total x n_total sparse)

• n_mesh: total number of nodes (vertices + midpoints)

• n_vertices: number of original mesh vertices

• n_midpoints: number of added midpoint nodes

• vertices: N x 2 matrix of all node coordinates

• triangles6: M x 6 connectivity matrix (columns: v0, v1, v2, mid01, mid12, mid20)