Linear Conforming and Nonconforming Upwind Finite Elements for the Convection-Diffusion Equation

Abstract

A conforming and a nonconforming method for the approximation of the stationary 2-D convection-diffusion equation at high Péclet number are presented. Convergence of order h is proved in a generic case and, for a particular choice of the upwind schemes, a discrete maximum principle is established under very unrestrictive conditions on the mesh. Results of numerical computations are produced to show the practical convergence of these methods.