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On the second-order convergence of a functionreconstructed from finite volume approximations of the Laplace equation onDelaunay-Voronoi meshes

Published online by Cambridge University Press:  30 November 2010

Pascal Omnes
Pascal Omnes*
Affiliation:
CEA, DEN, DM2S-SFME, 91191 Gif-sur-Yvette Cedex, France. pascal.omnes@cea.fr Université Paris 13, LAGA, CNRS UMR 7539, Institut Galilée, 99 avenue J.-B. Clément, 93430 Villetaneuse Cedex, France.
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Abstract

Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the right-hand side of the Laplace equation belongs to H1(Ω).

Keywords

Finite volume methodLaplace equationDelaunay meshesVoronoi meshesconvergenceerror estimates
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 4 , July 2011 , pp. 627 - 650
Copyright
© EDP Sciences, SMAI, 2010

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