Approximating Linear Poisson Solutions Using the Finite Element Method-Analysis and Computation

Abstract

Abstract This thesis treats Poisson's equation and its approximate solution using the nite element method. For this purpose, a general theory of the nite element method and its strategy are explained brie y. Then, Poisson's equation, its derivation and applications are explained in details. The nite element method is then applied to approximate the solution of Poisson's equation in one and two dimensional spaces. In this essence, error analysis is studied for the Poisson's equation in both categories, a posteriori and a priori error estimates. In addition, the thesis discusses the numerical solution for the Poisson's equation throughout examples in one and two dimensions using the MATLAB software. iv