Sufficient conditions for uniform convergence on layer-adapted grids Original Research Article

We study convergence properties of two upwind difference schemes for the solution of quasilinear convection–diffusion problems on layer-adapted grids. We derive conditions that are sufficient for convergence, uniformly in the perturbation parameter, of the methods. These conditions are easy to check and enable one to immediately deduce the rate of convergence. Numerical experiments support these theoretical results and indicate that the estimates are sharp.