Comparison Study Between Galerkin Finite Element Method and Finite Volume Method for Diffusion Problem

Abstract

The finite element method (FEM) is a robust and widely applied numerical scheme in the simulation of engineering problems, especially in structural mechanics. However, FEM is not as popular as the finite volume method (FVM) in Computational Fluid Dynamics (CFD), possibly due to its complicated numerical procedures. Indeed, FEM possesses tremendous advantages compared with FVM, particularly in dealing with complex geometry and rendering attractive flexibility to modify the interpolation functions. It is well-known that FEM and FVM differ in mathematical formulation, yet there is a lack of practical comparison between them. Therefore, the paper aims to develop a Galerkin FEM (GFEM) model, investigate its strengths and weaknesses compared with FVM, and discuss the conciliation between FEM and FVM. Our case study focuses on a two-dimensional diffusion problem comprising steady and transient cases, with and without heat generation. Our investigation revealed that GFEM does not possess conservative properties, which might yield spurious heat flux, leading to a 2 – 4% overestimation of the temperature field, depending on the amount of heat generation. Moreover, GFEM incurs approximately 34% higher computational time than FVM. However, FVM can be perceived as a special form of GFEM, and their relations were discussed.