COMPARISON OF CONTROL VOLUME AND GALERKIN FINITE ELEMENT METHODS FOR DIFFUSION-TYPE PROBLEMS

Abstract

Behavioral errors of an approximate solution, resulting from violation of fundamental physical constraints occurring in a diffusion transport phenomenon, are compared for Ike weighted residual-based and control volume-based finite element methods. Because of its physical background, the latter method offers a higher accuracy, better stability and oscillation characteristics, and preservation of the discrete maximum principle in coarse time-space discretization grids. Furthermore, it gives a simple, physically justified way for setting up a computationally convenient lumped mass matrix model in high-order finite element grids.