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Comptes Rendus Mathématique
Volume 353, n° 1
pages 31-34 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.013
Received : 11 July 2014 ;  accepted : 20 October 2014
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
 

Daniele A. Di Pietro a , Alexandre Ern b
a University Montpellier-2, I3M, 34057 Montpellier cedex 5, France 
b University Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France 

Abstract

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.

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Résumé

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.

The full text of this article is available in PDF format.


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