Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions

Abstract

We consider a singularly perturbed two-dimensional steady-state convection-diffusion problem with Robin boundary conditions. The coefficient of the highest-order terms in the differential equation and in the boundary conditions, denoted by ϵ, is a positive perturbation parameter, and so it may be arbitrarily small. Solutions to such problems present regular (exponential) boundary layers as well as corner layers. In this article, a numerical approach is carried out using a finite-difference technique with an appropriate layer-adapted piecewise-uniform Shishkin mesh to provide a good approximation of the exact solution. Some numerical examples are presented that show that the approximations obtained are accurate and that they are in agreement with the theoretical results.