A combined finite difference and local method of characteristic line approximation for convection-diffusion problems

A combined finite difference method and local method of characteristic line is presented for the numerical solution of singularly perturbed convection-diffusion problems. The method has discretization error estimates in maximum norm of second order, which holds uniformly in the singular perturbation parameter epsilon. In addition, it permits a fast iterative solution of the arising linear algebraic systems. The advantages of this technique are illustrated by numerical experiments in a two-dimensional square domain with outflow boundary layers.