Finite element approximation of convection diffusion problems using graded meshes Original Research Article

We consider the numerical approximation of a model convection–diffusion equation by standard bilinear finite elements. Using appropriately graded meshes we prove optimal order error estimates in the ε-weighted H1H1-norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. Finally, we present some numerical examples showing the good behavior of our method.