Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes

Abstract : Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive relations. We devise and analyze two families of such schemes for the Stokes equations in curl formulation, with the pressure degrees of freedom located at either mesh vertices or cells. The schemes ensure local mass and momentum conservation. We prove discrete stability by establishing novel discrete Poincaré inequalities. Using commutators related to the consistency error, we derive error estimates with first-order convergence rates for smooth solutions. We analyze two strategies for discretizing the external load, so as to deliver tight error estimates when the external load has a large curl-free or divergence-free part. Finally, numerical results are presented on three-dimensional polyhedral meshes.
Type de document :
Article dans une revue
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2015, 35 (4), pp.1672--1697. 〈10.1093/imanum/dru051〉
Liste complète des métadonnées

Littérature citée [45 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00939164
Contributeur : Jérôme Bonelle <>
Soumis le : vendredi 1 août 2014 - 18:05:50
Dernière modification le : mardi 6 mars 2018 - 15:58:28
Document(s) archivé(s) le : mardi 11 avril 2017 - 18:57:50

Fichier

Stokes-HAL-v2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Jérôme Bonelle, Alexandre Ern. Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2015, 35 (4), pp.1672--1697. 〈10.1093/imanum/dru051〉. 〈hal-00939164v2〉

Partager

Métriques

Consultations de la notice

422

Téléchargements de fichiers

204