MATLAB Finite Element Program for 2D Elliptic Equations with Rectangular Meshing

While 1D finite element programs are relatively straightforward, 2D finite element source codes present significant complexity. This MATLAB program solves two-dimensional elliptic equations using rectangular grid discretization, featuring robust implementation that generates both exact and numerical solution visualizations. The program serves as both an elliptic equation solver and a reference implementation for other PDEs, requiring only minor modifications to adapt to different equations. Key algorithmic components include mesh generation, stiffness matrix assembly, and variational formulation implementation.