Partial Differential Equations/Numerical Analysis
Error estimate for a 1D–2D finite volume scheme. Comparison with a standard scheme on a 2D non-admissible mesh
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 47-51.

We study a hybrid finite volume scheme to solve a problem set in a domain consisting of several zones of different dimensions in space. For a linear 1D–2D model problem, we define a specific H1 discrete norm and we state an error estimate in this norm. We compare the hybrid scheme to a classical scheme used on a 2D non-admissible mesh.

On étudie un schéma volumes finis hybride pour résoudre un problème posé dans un domaine où la dimension en espace est différente dʼune zone à lʼautre. Pour un problème modèle linéaire 1D–2D, nous définissons une norme H1 discrète 1D–2D adaptée, et nous établissons une estimation dʼerreur dans cette norme. Nous comparons le schéma hybride avec un schéma standard appliqué sur un maillage 2D non admissible.

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DOI: 10.1016/j.crma.2013.01.011
Viallon, Marie-Claude 1

1 Université de Lyon, UMR CNRS 5208, université Jean-Monnet, institut Camille-Jordan, faculté des sciences et techniques, 23, rue du Docteur-Paul-Michelon, 42023 Saint-Étienne cedex 2, France
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Viallon, Marie-Claude. Error estimate for a 1D–2D finite volume scheme. Comparison with a standard scheme on a 2D non-admissible mesh. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 47-51. doi : 10.1016/j.crma.2013.01.011. http://www.numdam.org/articles/10.1016/j.crma.2013.01.011/

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