A Comparison of Uniformly Convergent Difference Schemes for Two-Dimensional Convection-Diffusion Problems

Galerkin and Petrov Galerkin finite element methods are used to obtain new finite difference schemes for the solution of linear two-dimensional convection diffusion problems. Numerical estimates are made of the rates of convergence of these schemes, uniformly with respect to the perturbation parameter, and these uniform rates are shown to compare favourably with those of established methods.