Application of FEM and FDM in solving 2D irregular geometry heat transfer problem

Abstract

The study will focus on the application of finite element method (FEM) in solving two dimensional irregular geometry heat transfer problem. FEM is known as one of the numerical technique for finding approximate solutions to boundary value problems for differential equation. Therefore this method is a perfect application to solve a parabolic partial differential equation such as heat equation that describes the distribution of heat in a given region over time. In order to minimize an error function and produce a stable solution, FEM uses variation method or also known as the calculus of variations. All the solutions to this method related to the given problem will be compared with the solution from another popular numerical method which is finite difference method (FDM). FDM is also very useful in approximating the solutions to differential equation. However the application is limited to regular geometry and simple irregular geometry problems. The comparison of the solutions from these two methods will confirm that FEM is a better choice in solving two dimensional irregular geometry problems involving heat transfer.