Hybrid high-order methods for variable-diffusion problems on general meshes

Daniele A. Di Pietro; Alexandre Ern

doi:10.1016/j.crma.2014.10.013

Partial differential equations/Numerical analysis

Hybrid high-order methods for variable-diffusion problems on general meshes

Presented by: Olivier Pironneau

Daniele A. Di Pietro ¹; Alexandre Ern ²

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, Volume 353 (2015) no. 1, pp. 31-34.

Abstract
Résumé

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.

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.

Received: 2014-07-11
Accepted: 2014-10-20
Published online: 2014-11-03

DOI: 10.1016/j.crma.2014.10.013

Author's affiliations:

Daniele A. Di Pietro ¹; Alexandre Ern 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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     author = {Daniele A. Di Pietro and Alexandre Ern},
     title = {Hybrid high-order methods for variable-diffusion problems on general meshes},
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     pages = {31--34},
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     language = {en},
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Daniele A. Di Pietro; Alexandre Ern. Hybrid high-order methods for variable-diffusion problems on general meshes. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 31-34. doi : 10.1016/j.crma.2014.10.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.013/

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Cited by

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