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IMA Journal of Numerical Analysis Advance Access published online on June 16, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn084
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces

R. Eymard{dagger}

Université Paris-Est, 5 Bd Descartes, Champs-sur-Marne, F-77454 Marne la Vallée cedex 2, France

T. Gallouët{ddagger} and R. Herbin§

CMI, Université de Marseille, 39 rue Joliot Curie, F-13453 Marseille cedex 13, France

{dagger} Email: robert.eymard{at}univ-mlv.fr

{ddagger} Email: thierry.gallouet{at}cmi.univ-mrs.fr

§ Corresponding author. Email: raphaele.herbin{at}cmi.univ-mrs.fr

Received on 9 January 2008. Accepted for publication 7 November 2008.


  Abstract

A symmetric discretization scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces that may, for instance, be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell centred if no edge unknown is kept. It is shown to be accurate for several numerical examples. The convergence of the approximate solution to the continuous solution is proved for general (possibly discontinuous) tensors and general (possibly nonconforming) meshes and with no regularity assumption on the solution. An error estimate is then deduced under suitable regularity assumptions on the solution.

Key Words: heterogeneous anisotropic diffusion; nonconforming grids; finite-volume schemes


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