A conformal Petrov-Galerkin method for convection-dominated problems

Abstract

In this paper, we present the 'conformal Petrov-Galerkin' (CPG) method in order to solve the 2D convection-diffusion equation on meshes composed of triangular elements. By 'conformal' it is meant that the discrete system is obtained from the continuous weak formulation by appropriately selecting different finite-dimensional subspaces for the shape and test functions without any additional stabilizing term. Our approach is based on searching continuous test functions that provide exact nodal values for a selected class of solutions. This method induces a stabilizing upwinding effect that removes the wiggles obtained with the Galerkin method. Copyright © 2008 John Wiley & Sons, Ltd.