Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements

Alfredo Bermúdez; Pablo Gamallo; María R. Nogueiras; Rodolfo Rodríguez

doi:10.1016/j.crma.2005.03.023

Numerical Analysis

Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements

Presented by: Olivier Pironneau

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

Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 687-692.

Abstract (Original language)
Résumé

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.

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.

Received: 2004-11-24
Accepted: 2005-03-22
Published online: 2005-05-01

DOI: 10.1016/j.crma.2005.03.023

Author's affiliations:

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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     title = {Approximation properties of lowest-order hexahedral {Raviart{\textendash}Thomas} finite elements},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {687--692},
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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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