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Convergence analysis for an exponentially fittedFinite Volume Method

Published online by Cambridge University Press:  15 April 2002

Reiner Vanselow
Reiner Vanselow*
Affiliation:
Dresden University of Technology, Department of Mathematics, 01062 Dresden, Germany. (vanselow@math.tu-dresden.de)
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Abstract

The paper is devoted to the convergence analysis of a well-knowncell-centered Finite Volume Method (FVM) for aconvection-diffusion problem in $\mathbb{R}^2$ . This FVM is based on Voronoi boxes andexponential fitting. To prove the convergence of the FVM, we usea new nonconforming Petrov-Galerkin Finite Element Method (FEM)for which the system of linear equations coincides completely withthat of the FVM. Thus, by proving convergence properties of theFEM we obtain similar ones for the FVM. For the error estimationof the FEM well-known statements have to be modified.

Keywords

Convection-diffusion problemcell-centered finite volume methodVoronoi boxesexponential fittingconvergence analysisnonconforming finite element method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1165 - 1188
Copyright
© EDP Sciences, SMAI, 2000

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