On the Choice of Parameters in Stabilization Methods for Convection–Diffusion Equations

Abstract

A popular finite element approach for the numerical solution of convection–diffusion equations is the streamline upwind/Petrov–Galerkin (SUPG) method. Unfortunately, in the convection–dominated regime, the SUPG solution often contains spurious oscillations along sharp layers. A possible remedy is to introduce an additional artificial diffusion term in the SUPG discretization. We call such approaches spurious oscillations at layers diminishing (SOLD) methods. The properties of the SOLD methods are significantly influenced by the choice of the respective stabilization parameter which determines the amount of the artificial diffusion. The aim of this paper is to discuss various definitions of these stabilization parameters.