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Convergence rate of a finite volume schemefor a two dimensional convection-diffusion problem

Published online by Cambridge University Press:  15 August 2002

Yves Coudière ,
Jean-Paul Vila  and
Philippe Villedieu
Yves Coudière
Affiliation:
Mathematiques pour l'Industrie et la Physique, UMR CNRS-UPS 5640, INSA, Domaine Scientifique de Rangueil, 31077 Toulouse Cedex 4, France.
Jean-Paul Vila
Affiliation:
Mathematiques pour l'Industrie et la Physique, UMR CNRS-UPS 5640, INSA, Domaine Scientifique de Rangueil, 31077 Toulouse Cedex 4, France.
Philippe Villedieu
Affiliation:
ONERA, Centre de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse Cedex, France.
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Abstract

In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate oforder h, assuming only the W2,p (for p>2) regularity of thecontinuous solution, on a mesh of quadrangles. The proof is based on anextension of the ideas developed in [12]. Some newdifficulties arise here, due to the weak regularity of the solution, and thenecessity to approximate the entire gradient, and not only its normalcomponent, as in [12].

Keywords

Finite volumesconvection diffusionconvergence rateunstructured meshes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 3 , May 1999 , pp. 493 - 516
Copyright
© EDP Sciences, SMAI, 1999

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