Finite Element Heat Conduction

FEM Triangulation · Laplace/Poisson Equation · Stiffness Matrix · Click to Set BCs

Boundary Condition Mode

Click on the domain to set boundary conditions. Then click Solve FEM to compute temperature distribution.

Parameters

10
1.0
0.0

Stiffness Matrix Sparsity

Temperature Profile

FEM Theory

Poisson: −∇·(k∇T) = f in Ω
Weak form: ∫k∇T·∇v dΩ = ∫fv dΩ
Stiffness matrix K_{ij} = ∫k ∇φ_i·∇φ_j dΩ
Linear system: KT = F
Triangle elements: φ_i = 1 on node i, 0 on others
Piecewise-linear → 1st-order FEM
Sparsity: ~6 entries per row (local support)
Solved via Gauss-Seidel iteration