The application of finite element method in 2d heat distribution problems for irregular geometry

Abstract

In mathematics, the finite element method (FEM) is a numerical technique for finding approximate solutions of boundary value problems from differential equations. The term ‘finite element’ stems from the procedure in which a structure is divided into small but finite size elements. FEM is very useful for problems with complicated geometries, loadings, and material properties where analytical solutions cannot be obtained. In this research, simple irregular problem is used as an example of industry problems to be solved using FEM and finite difference method (FDM). Matlab programming is used as a calculation medium for both FEM and FDM methods respectively. Since the results of the problem for both methods converge, it also proves that the results are valid. Hence we can conclude that simple irregular problem can be solved using FEM and FDM. From this research, we also discovered that FEM produces more stable and consistent result compared to FDM for the solution of simple irregular problem and the results are presented in graphs.