Nous démontrons que l'hypothèse de la petitesse du paramètre de marquage θ dans les méthodes d'éléments finis adaptatives peut être évitée dans la démonstration de l'optimalité de l'algorithme. Pour cela, nous introduisons une nouvelle technique basée sur la comparaison de différentes solutions correspondant à des espaces obtenus par différents raffinements d'un maillage donné. On considère des méthodes conformes et non conformes de bas degé sur des maillages en triangles et tetraèdres.
We show that the standard assumption on the smallness of the marking parameter θ in adaptive finite element methods can be avoided for the proof of the optimality of the algorithm. To this end we propose a new technique based on comparison of the solutions of different finite element spaces obtained by different refinements of a given mesh. We consider conforming and nonconforming low-order finite elements on triangular and tetrahedral meshes.
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@article{CRMATH_2011__349_3-4_225_0,
author = {Becker, Roland and Trujillo, David},
title = {A remark on the optimality of adaptive finite element methods},
journal = {Comptes Rendus. Math\'ematique},
pages = {225--228},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.11.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.11.011/}
}
TY - JOUR AU - Becker, Roland AU - Trujillo, David TI - A remark on the optimality of adaptive finite element methods JO - Comptes Rendus. Mathématique PY - 2011 SP - 225 EP - 228 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.11.011/ DO - 10.1016/j.crma.2010.11.011 LA - en ID - CRMATH_2011__349_3-4_225_0 ER -
%0 Journal Article %A Becker, Roland %A Trujillo, David %T A remark on the optimality of adaptive finite element methods %J Comptes Rendus. Mathématique %D 2011 %P 225-228 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.11.011/ %R 10.1016/j.crma.2010.11.011 %G en %F CRMATH_2011__349_3-4_225_0
Becker, Roland; Trujillo, David. A remark on the optimality of adaptive finite element methods. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 225-228. doi : 10.1016/j.crma.2010.11.011. http://www.numdam.org/articles/10.1016/j.crma.2010.11.011/
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