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

Abstract 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 orderN−1 ln Nin a global energy norm and of orderN−1/2ln3/2 Npointwise near the outflow boundary, where the total number of mesh points isO(N2).