Numerical solution of a mixed singularly perturbed parabolic–elliptic problem

A one-dimensional singularly perturbed problem of mixed type is considered. The domain under consideration is partitioned into two subdomains. In the first subdomain a parabolic reaction– diffusion problem is given and in the second one an elliptic convection–diffusion–reaction problem. The solution is decomposed into regular and singular components. The problem is discretized using an inverse-monotone finite volume method on condensed Shishkin meshes. We establish an almost second-order global pointwise convergence in the space variable, that is uniform with respect to the perturbation parameter. © 2005 Elsevier Inc. All rights reserved.