Finite Element Method Solution For Two Dimesiona Partial Differential Elliptic Equation

Abstract

This thesis focuses on solving two-dimensional elliptic partial differential equations, namely the Laplace and Poisson equations, using the Galerkin finite element method. Elliptic partial differential equation is a class of partial differential equations describing phenomena that do not change from moment to moment, as when a flow of heat or fluid takes place within a medium with no accumulations. The Galerkin finite element method is a numerical technique for solving partial differential equations. It is based on the idea of approximating the exact solution of a PDE by a finite dimensional function space spanned by a set of basis functions. MATLAB, a popular programming language for technical computing, was used to implement the method and generate the resulting figures and tables. The accuracy of the numerical results was evaluated by comparing them to the exact solution, and the resulting error demonstrated the effectiveness of the finite element method. Furthermore, increasing the number of elements resulted in a reduction in the error, indicating a convergence towards the exact solution