Uniformly convergent finite volume difference scheme for 2D convection-dominated problem with discontinuous coefficients

Abstract

Two dimensional singularly perturbed convection-diffusion problem with discontinuous coefficients is considered. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We established first-order global pointwise convergence that is uniform with respect to the perturbation parameter. Numerical experiments that support the theoretical results are given. © 2004 Elsevier Inc. All rights reserved.