Hybrid High-Order methods for variable diffusion problems on general meshes

Daniele Antonio Di Pietro (1) , Alexandre Ern (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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.

Mots clés: variable diffusion; hybrid high-order methods; general meshes

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Alexandre Ern. Hybrid High-Order methods for variable diffusion problems on general meshes. Comptes Rendus. Mathématique, 2014, 353, pp.31--34. ⟨10.1016/j.crma.2014.10.013⟩. ⟨hal-01023302⟩