[Une évaluation monotone de brones fiables pour la constante inf-sup dans la méthode de l'approximation des bases réduites]
Un ingrédient fondamental de l'analyse a posteriori pour l'approximation par méthode par bases réduites de problèmes coercifs ou non coercifs est la définition de bornes fiables pour la constante de coercivité ou la constante inf-sup. Dans cette Note, nous généralisons et améliorons la méthode d'optimisation linéaire de contraintes successives présentées dans Huynh (2007), en proposant une version monotone de cet algorithme qui conduit à la fois à des évaluations plus stables et un nombre réduit de calculs hors ligne.
For accurate a posteriori error analysis of the reduced basis method for coercive and non-coercive problems, a critical ingredient lies in the evaluation of a lower bound for the coercivity or inf-sup constant. In this short Note, we generalize and improve the successive constraint method first presented by Huynh (2007) by providing a monotonic version of this algorithm that leads to both more stable evaluations and fewer offline computations.
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@article{CRMATH_2008__346_23-24_1295_0,
author = {Chen, Yanlai and Hesthaven, Jan S. and Maday, Yvon and Rodr{\'\i}guez, Jer\'onimo},
title = {A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1295--1300},
publisher = {Elsevier},
volume = {346},
number = {23-24},
year = {2008},
doi = {10.1016/j.crma.2008.10.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.10.012/}
}
TY - JOUR AU - Chen, Yanlai AU - Hesthaven, Jan S. AU - Maday, Yvon AU - Rodríguez, Jerónimo TI - A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations JO - Comptes Rendus. Mathématique PY - 2008 SP - 1295 EP - 1300 VL - 346 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.10.012/ DO - 10.1016/j.crma.2008.10.012 LA - en ID - CRMATH_2008__346_23-24_1295_0 ER -
%0 Journal Article %A Chen, Yanlai %A Hesthaven, Jan S. %A Maday, Yvon %A Rodríguez, Jerónimo %T A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations %J Comptes Rendus. Mathématique %D 2008 %P 1295-1300 %V 346 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.10.012/ %R 10.1016/j.crma.2008.10.012 %G en %F CRMATH_2008__346_23-24_1295_0
Chen, Yanlai; Hesthaven, Jan S.; Maday, Yvon; Rodríguez, Jerónimo. A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations. Comptes Rendus. Mathématique, Tome 346 (2008) no. 23-24, pp. 1295-1300. doi : 10.1016/j.crma.2008.10.012. http://www.numdam.org/articles/10.1016/j.crma.2008.10.012/
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