A finite difference method for a singularly perturbed 2-D elliptic convection-diffusion PDEs on Shishkin-type meshes with non-smooth convection and source terms

This paper deals with a class of singularly perturbed 2-D elliptic convection-diffusion PDEs with non-smooth convection and source terms. The discontinuity in the convection and source terms portray corner and interior layers in the solution. This type of model problem often appears in modeling various physical phenomena, particularly, in mathematical biology, and thus requires effective numerical techniques for analyzing them computationally. For this purpose, we approximate the considered linear problem by developing an efficient numerical method. The spatial discretization for the numerical method is based on a finite difference scheme. The spatial domain is discretized by appropriate layer-adapted meshes (S-mesh and B-S-mesh) to accomplish this. The theoretical outcomes are finally supported by extensive numerical experiments, which also include a comparison of the proposed numerical method in terms of the order of accuracy and the computational cost.