A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layers

In this article, we investigate a two-dimensional (2-D) singularly perturbed convection-reaction-diffusion elliptic type problem where two parameters epsilon and mu multiply the diffusion and convection terms, respectively. Furthermore, we assume that jump discontinuities exist in the source term along the x- and y-axis. Due to the presence of perturbation parameters, the solutions to such problems show boundary and corner layers. Moreover, the discontinuity in the source term adds the interior layers to the solution whose suitable numerical approach is the important goal of this article. A numerical approach is carried out using an upwind finite-difference technique that includes an appropriate layer-adapted piecewise uniform Shishkin mesh. Some examples are presented which show the good performance of the proposed method and the agreement with the theoretical analysis.(c) 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).