General Finite Element Program for Solving Poisson Problems (Linear Elements)

This document presents a general finite element program designed for solving Poisson problems using linear elements. The compressed package includes a practical implementation (exp.m) that can be executed directly in MATLAB environment. The code employs standard finite element methodology with linear shape functions for discretization. If computational efficiency requires improvement, users can optimize results by adjusting the mesh parameter h to achieve better convergence rates. The program demonstrates core finite element techniques including stiffness matrix assembly, load vector computation, and boundary condition handling. For solving other types of problems, similar coding approaches can be adopted to implement finite element solutions. This program provides an efficient and straightforward method for Poisson problem resolution, with potential applications across various fields including engineering, mathematics, and physics. The implementation showcases key MATLAB functions for matrix operations and numerical integration essential for finite element analysis.