Volume 13, pp. 1-11, 2002.

A uniformly accurate finite volume discretization for a convection-diffusion problem

Dirk Wollstein, Torsten Linss, and Hans-Görg Roos

Abstract

A singularly perturbed convection-diffusion problem is considered. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We establish first-order convergence in a global energy norm and a mesh-dependent discrete energy norm, no matter how small the perturbation parameter. Numerical experiments support the theoretical results.

Full Text (PDF) [136 KB]

Key words

convection-diffusion problems, finite volume methods, singular perturbation, Shishkin mesh.

AMS subject classifications

65N30.

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