This Note is devoted to the presentation of a linear diffusion scheme that respects the maximum principle on very distorted meshes. The main idea is to use a classical Finite Volumes scheme and to perform a first integration on the Voronoï mesh based on the centers of the cells. A second integration on the primary mesh is then performed. By construction the scheme preserves the maximum principle. A numerical example is also given.
Cette Note est consacrée à la présentation d'un schéma de diffusion qui respecte le principe du maximum sur des maillages très déformés. L'idée essentielle consiste à utiliser un schéma de Volumes Finis classique sur le maillage de Voronoï basé sur les barycentres des mailles primales. On procède alors à une deuxième intégration sur les mailles primales. Par construction, le schéma respecte le principe du maximum. Un exemple numérique est fourni.
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@article{CRMATH_2009__347_21-22_1317_0,
author = {Siess, Vincent},
title = {A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes},
journal = {Comptes Rendus. Math\'ematique},
pages = {1317--1320},
publisher = {Elsevier},
volume = {347},
number = {21-22},
year = {2009},
doi = {10.1016/j.crma.2009.10.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.004/}
}
TY - JOUR AU - Siess, Vincent TI - A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes JO - Comptes Rendus. Mathématique PY - 2009 SP - 1317 EP - 1320 VL - 347 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.10.004/ DO - 10.1016/j.crma.2009.10.004 LA - en ID - CRMATH_2009__347_21-22_1317_0 ER -
%0 Journal Article %A Siess, Vincent %T A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes %J Comptes Rendus. Mathématique %D 2009 %P 1317-1320 %V 347 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.10.004/ %R 10.1016/j.crma.2009.10.004 %G en %F CRMATH_2009__347_21-22_1317_0
Siess, Vincent. A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1317-1320. doi : 10.1016/j.crma.2009.10.004. http://www.numdam.org/articles/10.1016/j.crma.2009.10.004/
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