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.
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@article{CRMATH_2015__353_1_31_0, author = {Di Pietro, Daniele A. and Ern, Alexandre}, title = {Hybrid high-order methods for variable-diffusion problems on general meshes}, journal = {Comptes Rendus. Math\'ematique}, pages = {31--34}, publisher = {Elsevier}, volume = {353}, number = {1}, year = {2015}, doi = {10.1016/j.crma.2014.10.013}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2014.10.013/} }
TY - JOUR AU - Di Pietro, Daniele A. AU - Ern, Alexandre TI - Hybrid high-order methods for variable-diffusion problems on general meshes JO - Comptes Rendus. Mathématique PY - 2015 SP - 31 EP - 34 VL - 353 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2014.10.013/ DO - 10.1016/j.crma.2014.10.013 LA - en ID - CRMATH_2015__353_1_31_0 ER -
%0 Journal Article %A Di Pietro, Daniele A. %A Ern, Alexandre %T Hybrid high-order methods for variable-diffusion problems on general meshes %J Comptes Rendus. Mathématique %D 2015 %P 31-34 %V 353 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2014.10.013/ %R 10.1016/j.crma.2014.10.013 %G en %F CRMATH_2015__353_1_31_0
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://archive.numdam.org/articles/10.1016/j.crma.2014.10.013/
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