Robustness of an Upwind Finite Difference Scheme for Semilinear Convection-Diffusion Problems with Boundary Turning Points

Abstract

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposition is used to analyse the convergence of an upwind finite difference scheme on Shishkin meshes.