Finite Element Convergence Studies of a Time-Dependent Test Problem Using COMSOL 5.1

Abstract

The finite element method (FEM) is a well known numerical method in solving partial differential equations (PDEs). All numerical methods inherently have error in comparison to the true solution of the PDE. Base on the FEM theory, the appropriate norm of this error is bounded and it can be estimated by the mesh size. One standard method to get an idea about the sensibility of the numerical solution is to do convergence studies on the method. More precisely, compare the results obtained from two consecutive mesh refinements. This comparison, then can be quantified using theory of FEM by obtaining the convergence order. In this paper we carry out convergence studies for the time-dependent parabolic test problem (the heat transfer equation) and investigate the effect of ODE solver on the behavior of the convergence of the method using commercial FEM software COMSOL 5.1.