Comptes Rendus
no. 9-10
Numerical Analysis
Accurate a posteriori error evaluation in the reduced basis method
Presented by: Olivier Pironneau
Fabien Casenave1
1Université Paris-Est, CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 539-542

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.05.012

Fabien Casenave  1

1 Université Paris-Est, CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France 
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Fabien Casenave. Accurate a posteriori error evaluation in the reduced basis method. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 539-542. doi: 10.1016/j.crma.2012.05.012

[1] C. Canuto; T. Tonn; K. Urban 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] L. Machiels; Y. Maday; I.B. Oliveira; A.T. Patera; D.V. Rovas 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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