no. 1
Partial differential equations/Numerical analysis
Hybrid high-order methods for variable-diffusion problems on general meshes
[Méthodes hybrides d'ordre élevé pour des problèmes à diffusion variable sur des maillages généraux]

Présenté par : Olivier Pironneau

Di Pietro, Daniele A.1 ; Ern, Alexandre2
1 University Montpellier-2, I3M, 34057 Montpellier cedex 5, France
2 University Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France
Comptes Rendus. Mathématique, Tome 353 (2015) no. 1, pp. 31-34.

Nous étendons la méthode hybride d'ordre élevé conçue par les auteurs pour le problème de Poisson à des problèmes de diffusion hétérogène/anisotrope. La pierre angulaire est une reconstruction locale du gradient discret à partir des degrés de liberté polynomiaux sur les éléments et les faces. On établit des estimations d'erreur optimales.

We extend the Hybrid High-Order method introduced by the authors for the Poisson problem to problems with heterogeneous/anisotropic diffusion. The cornerstone is a local discrete gradient reconstruction from element- and face-based polynomial degrees of freedom. Optimal error estimates are proved.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.013
Di Pietro, Daniele A. 1 ; Ern, Alexandre 2

1 University Montpellier-2, I3M, 34057 Montpellier cedex 5, France
2 University Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France 
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Di Pietro, Daniele A.; Ern, Alexandre. Hybrid high-order methods for variable-diffusion problems on general meshes. Comptes Rendus. Mathématique, Tome 353 (2015) no. 1, pp. 31-34. doi : 10.1016/j.crma.2014.10.013. http://www.numdam.org/articles/10.1016/j.crma.2014.10.013/

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