Comptes Rendus
no. 17-18
Numerical Analysis
Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes
[Convergence du schéma volume fini multi-point de type “O” pour les problèmes de diffusion hétérogène anisotrope sur maillages généraux]

Présenté par : Olivier Pironneau

Leo Agelas1 ; Roland Masson1
1 Institut français du petrole, Division technologie, information, 1 et 4, avenue de Bois Préau, 92852 Rueil Malmaison, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1007-1012.

Cette Note démontre la convergence du schéma volume fini de type « O » pour les problèmes de diffusion en milieu hétérogène anisotrope. Sa principale originalité est de traiter des maillages polygonaux et polyédriques généraux ainsi que des coefficients de diffusion L∞, ce qui est essentiel dans les applications.

This Note proves the convergence of the finite volume MultiPoint Flux Approximation (MPFA) O scheme for anisotropic and heterogeneous diffusion problems. Its main originality is that our framework and proof deal with general polygonal and polyhedral meshes as well as with L∞ diffusion coefficients, which is essential in practical applications.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.07.015
Leo Agelas 1 ; Roland Masson 1

1 Institut français du petrole, Division technologie, information, 1 et 4, avenue de Bois Préau, 92852 Rueil Malmaison, France 
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Leo Agelas; Roland Masson. Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1007-1012. doi : 10.1016/j.crma.2008.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.015/

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[2] I. Aavatsmark; G.T. Eigestad; R.A. Klausen; M.F. Wheeler; I. Yotov Convergence of a symmetric MPFA method on quadrilateral grids, Comput. Geosci., Volume 11 (2007), pp. 333-345

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[9] D. Gunasekera, P. Childs, J. Herring, J. Cox, A multi-point flux discretization scheme for general polyhedral grids, SPE 48855, in: Proc. SPE 6th International Oil and Gas Conference and Exhibition, China, November 1998

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