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 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 is proved for regular families of asymptotically parallelepiped meshes. The need of the asymptotically parallelepiped assumption is demonstrated with a numerical example.
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@article{CRMATH_2005__340_9_687_0, author = {Berm\'udez, Alfredo and Gamallo, Pablo and Nogueiras, Mar{\'\i}a R. and Rodr{\'\i}guez, Rodolfo}, title = {Approximation properties of lowest-order hexahedral {Raviart{\textendash}Thomas} finite elements}, journal = {Comptes Rendus. Math\'ematique}, pages = {687--692}, publisher = {Elsevier}, volume = {340}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.03.023}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2005.03.023/} }
TY - JOUR AU - Bermúdez, Alfredo AU - Gamallo, Pablo AU - Nogueiras, María R. AU - Rodríguez, Rodolfo TI - Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements JO - Comptes Rendus. Mathématique PY - 2005 SP - 687 EP - 692 VL - 340 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.03.023/ DO - 10.1016/j.crma.2005.03.023 LA - en ID - CRMATH_2005__340_9_687_0 ER -
%0 Journal Article %A Bermúdez, Alfredo %A Gamallo, Pablo %A Nogueiras, María R. %A Rodríguez, Rodolfo %T Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements %J Comptes Rendus. Mathématique %D 2005 %P 687-692 %V 340 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.03.023/ %R 10.1016/j.crma.2005.03.023 %G en %F CRMATH_2005__340_9_687_0
Bermúdez, Alfredo; Gamallo, Pablo; Nogueiras, María R.; Rodríguez, Rodolfo. Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 687-692. doi : 10.1016/j.crma.2005.03.023. http://www.numdam.org/articles/10.1016/j.crma.2005.03.023/
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