Uniform convergence of discretization error for a singular perturbation problem

Cell-centered discretization of the convection-diffusion equation with large Péclet number Pe is analyzed, in the presence of a parabolic boundary layer. It is shown theoretically how, by suitable mesh refinement in the boundary layer, the accuracy can be made to be uniform in Pe, at the cost of a IogPe increase of the number of grid cells, in the case of upwind discretization. Numerical experiments are presented indicating that this can in practice also be achieved with a Pe-independent number of grid cells, both with upwind and central discretization, and with vertex-centered discretization. © 1996 John Wiley & Sons, Inc.