Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations

Abstract

We study a system of coupled convection-diffusion equations. The equations have diffusion parameters of different magnitudes associated with them which give rise to boundary layers at either boundary. An upwind finite difference scheme on arbitrary meshes is used to solve the system numerically. A general error estimate is derived that allows to immediately conclude robust convergence – w.r.t. the perturbation parameters – for certain layer-adapted meshes, thus improving and generalising previous results [4]. We present the results of numerical experiments to illustrate our theoretical findings.