Dans la méthode des bases réduites, lʼévaluation de lʼestimateur a posteriori peut sʼavérer particulièrement sensible aux erreurs dʼarrondis machine. Dans cette Note, lʼorigine de la perte de précision est révélée et une solution à ce problème est proposée et illustrée sur un exemple simple.
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this Note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.
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@article{CRMATH_2012__350_9-10_539_0, author = {Casenave, Fabien}, title = {Accurate a posteriori error evaluation in the reduced basis method}, journal = {Comptes Rendus. Math\'ematique}, pages = {539--542}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.05.012}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.05.012/} }
TY - JOUR AU - Casenave, Fabien TI - Accurate a posteriori error evaluation in the reduced basis method JO - Comptes Rendus. Mathématique PY - 2012 SP - 539 EP - 542 VL - 350 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.05.012/ DO - 10.1016/j.crma.2012.05.012 LA - en ID - CRMATH_2012__350_9-10_539_0 ER -
%0 Journal Article %A Casenave, Fabien %T Accurate a posteriori error evaluation in the reduced basis method %J Comptes Rendus. Mathématique %D 2012 %P 539-542 %V 350 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.05.012/ %R 10.1016/j.crma.2012.05.012 %G en %F CRMATH_2012__350_9-10_539_0
Casenave, Fabien. Accurate a posteriori error evaluation in the reduced basis method. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 539-542. doi : 10.1016/j.crma.2012.05.012. http://archive.numdam.org/articles/10.1016/j.crma.2012.05.012/
[1] A posteriori error analysis of the reduced basis method for nonaffine parametrized nonlinear PDEs, SIAM J. Numer. Anal., Volume 47 (2009), pp. 2001-2022
[2] Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, C. R. Acad. Sci. Paris, Ser. I, Volume 331 (2000) no. 2, pp. 153-158
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