A Study of Finite Element Method for Laplace Equation

This paper aims at treating the Finite element method (FEM) for the discretization of elliptic Partial differential equation (PDE) and focuses on FEM for solving two-dimensional Laplace equation in a sub-set of a square domain.The idea is to use finite element spaces that are induced by triangulations of a square domain to discretize the two dimensional elliptic Laplace equation on the surface. Then the two numerical solutions obtained by FEM based on the number of finite elements are compared to check the accuracy of the developed scheme. The FEM MATLAB Programming is used for the solution of two dimensional Laplace equations. Results are then compared with the analytic solution to check the accuracy of the developed scheme.