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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Robert Eymard 1; Thierry Gallouët 2; Raphaèle Herbin 2
@article{CRMATH_2004__339_4_299_0, author = {Robert Eymard and Thierry Gallou\"et and Rapha\`ele Herbin}, title = {A finite volume scheme for anisotropic diffusion problems}, journal = {Comptes Rendus. Math\'ematique}, pages = {299--302}, publisher = {Elsevier}, volume = {339}, number = {4}, year = {2004}, doi = {10.1016/j.crma.2004.05.023}, language = {en}, }
TY - JOUR AU - Robert Eymard AU - Thierry Gallouët AU - Raphaèle Herbin TI - A finite volume scheme for anisotropic diffusion problems JO - Comptes Rendus. Mathématique PY - 2004 SP - 299 EP - 302 VL - 339 IS - 4 PB - Elsevier DO - 10.1016/j.crma.2004.05.023 LA - en ID - CRMATH_2004__339_4_299_0 ER -
Robert Eymard; Thierry Gallouët; Raphaèle Herbin. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.05.023/
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[4] 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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