Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter c, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates E-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the E-uniform convergence in the global maximum norm of the approximatioris generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results. (C) 2005 Elsevier Ltd. All rights reserved.