Numerical Analysis
A finite volume scheme for anisotropic diffusion problems
Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 299-302.

A new finite volume for the discretization of anisotropic diffusion problems on general unstructured meshes in any space dimension is presented. The convergence of the approximate solution and its discrete gradient is proven. The efficiency of the scheme is illustrated by numerical results.

On présente ici un nouveau schéma volumes finis pour la discrétisation des équations de diffusion anisotropes sur des maillages non structurés, pour toute dimension d'espace. On prouve la convergence de la solution approchée, ainsi que celle d'un gradient approché. La pertinence du schéma est illustrée par des résultats numériques.

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DOI: 10.1016/j.crma.2004.05.023
Eymard, Robert 1; Gallouët, Thierry 2; Herbin, Raphaèle 2

1 Université de Marne-la-Vallée, Cité Descartes, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
2 Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France
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Eymard, Robert; Gallouët, Thierry; Herbin, Raphaèle. A finite volume scheme for anisotropic diffusion problems. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 299-302. doi : 10.1016/j.crma.2004.05.023. http://www.numdam.org/articles/10.1016/j.crma.2004.05.023/

[1] Eymard, R.; Gallouët, T. H-convergence and numerical schemes for elliptic equations, SIAM J. Numer. Anal., Volume 41 (2003) no. 2, pp. 539-562

[2] Eymard, R.; Gallouët, T.; Herbin, R. Finite volume methods (Ciarlet, P.G.; Lions, J.L., eds.), Handbook of Numerical Analysis, vol. VII, North-Holland, 2000, pp. 713-1020

[3] Eymard, R.; Gallouët, T.; Herbin, R. Finite volume approximation of elliptic problems and convergence of an approximate gradient, Appl. Numer. Math., Volume 37 (2001) no. 1–2, pp. 31-53

[4] Herbin, R.; Marchand, E. Finite volume approximation of a class of variational inequalities, IMA J. Numer. Anal., Volume 21 (2001) no. 2, pp. 553-585

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