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Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes

Published online by Cambridge University Press:  15 April 2002

Yves Coudière  and
Philippe Villedieu
Yves Coudière
Affiliation:
Mathématiques pour l'Industrie et la Physique, UMR 5640, INSA, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France. ([email protected])
Philippe Villedieu
Affiliation:
ONERA, Centre de Toulouse, 2 avenue Ed. Belin, 31055 Toulouse Cedex 4, France. ([email protected])
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Abstract

We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes of size h).

Keywords

Finite volumesmesh refinementconvection-diffusionconvergence rate.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1123 - 1149
Copyright
© EDP Sciences, SMAI, 2000

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