Implementation of Finite Element Method

Abstract

The finite element method is a numerical technique used to perform finite element analysis of any given physical phenomenon. Finite element method is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation and the growth of biological cells etc. Here, in this thesis we showed the implementation of finite element method with the help of boundary value problem and the galerkin methods. Galerkin methods are a class of methods for converting a continuous operator problem to a discrete problem. In this thesis we used galerkin finite element method solution to solve 2D boundary valued problem using triangular elements. We developed a Matlab code to solve 2D boundary value problem. Then we got analytical and numerical solutions with proper figures. You will see those solutions and figures in our thesis paper.