Comptes Rendus
no. 6
Numerical analysis
An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems
[Estimateur a posteriori pour les problèmes aux valeurs propres hermitiens positifs, reposant sur des décalages]

Présenté par : Olivier Pironneau

Athmane Bakhta1 ; Damiano Lombardi2
1 École des ponts ParisTech, France
2 INRIA, France
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 696-705.

L'objet de ce travail est la mise au point et l'étude d'un estimateur a posteriori pour les problèmes aux valeurs propres hermitiens positifs. L'estimateur proposé se base sur une approximation de la rélation entre l'erreur et le résidu du problème. Les propriétés mathématiques de l'estimateur sont étudiées. Des experiences numériques sont proposées afin de valider l'estimateur.

This work deals with an a posteriori error estimator for Hermitian positive eigenvalue problems. The proposed estimator is based on the residual and the definition of suitable shifts in the matrix spectrum. The mathematical properties (certification and sharpness) are investigated and some numerical experiments are proposed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.04.017

Athmane Bakhta 1 ; Damiano Lombardi 2

1 École des ponts ParisTech, France
2 INRIA, France 
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Athmane Bakhta; Damiano Lombardi. An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 696-705. doi : 10.1016/j.crma.2018.04.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.017/

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