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

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 E, 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. (c) 2023 The Author(s). Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc -nd /4 .0/).