A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem

A Galerkin finite element method that uses piecewise bilinears on a simple piecewise equidistant mesh is applied to a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation parameter, of order Ny1 ln N in a global energy norm and of order Ny1r2 ln3r2 N pointwise near the outflow boundary, where the total number of mesh points is O N2 ..