Comptes Rendus
no. 9
Numerical Analysis
Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements
[Proprietés d'approximation des éléments finis de Raviart–Thomas hexaédriques d'ordre le plus bas]

Présenté par : Olivier Pironneau

Alfredo Bermúdez1 ; Pablo Gamallo2 ; María R. Nogueiras1 ; Rodolfo Rodríguez3
1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2 Institute of Sound and Vibration Research, University of Southampton, Highfield Road, Southampton SO17 1BJ, UK
3 GI
Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 687-692.

Nous démontrons quelques résultats d'interpolation pour les éléments finis de Raviart–Thomas hexaédriques d'ordre le plus bas. Nous prouvons convergence dans l'espace H(div) pour des familles régulières de maillages dont les éléments sont, asymptotiquement, des parallélépipèdes. La nécessité de cette hypothèse est montrée numériquement avec un exemple.

Basic interpolation results are settled for lowest-order hexahedral Raviart–Thomas finite elements. Convergence in H(div) is proved for regular families of asymptotically parallelepiped meshes. The need of the asymptotically parallelepiped assumption is demonstrated with a numerical example.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.03.023
Alfredo Bermúdez 1 ; Pablo Gamallo 2 ; María R. Nogueiras 1 ; Rodolfo Rodríguez 3

1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2 Institute of Sound and Vibration Research, University of Southampton, Highfield Road, Southampton SO17 1BJ, UK
3 GI 
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     journal = {Comptes Rendus. Math\'ematique},
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Alfredo Bermúdez; Pablo Gamallo; María R. Nogueiras; Rodolfo Rodríguez. Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 687-692. doi : 10.1016/j.crma.2005.03.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.023/

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