A successive constraint method with minimal offline constraints for lower bounds of parametric coercivity constant

Sylvain Vallaghé (1) , Michel Fouquembergh (2) , Annabelle Le Hyaric (2) , Christophe Prud'Homme (3, 4)

1 MGMI - Modélisation Géométrique & Multirésolution pour l'Image
2 EADS IW - EADS Innovation Works [Suresnes]
3 IRMA - Institut de Recherche Mathématique Avancée
4 EDP - Equations aux Dérivées Partielles

A posteriori error estimates are a key ingredient for the certified reduced basis method. Sharp error bounds rely on the construction of lower bounds for the coercivity or inf-sup stability constant. The Successive Constraint Method (SCM) has been previously proposed to compute such lower bounds, using an efficient Offline-Online strategy. We present in this article some modifications to the SCM to get rid of user-dependent parameters, which also improve convergence and reduce the computational cost of the method.

Mots clés: successive constraints methods; certified reduced basis; linear programming; generalized eigenvalue problems

Domaines: Analyse numérique [math.NA]; Thermique [physics.class-ph]; Thermique [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Sylvain Vallaghé, Michel Fouquembergh, Annabelle Le Hyaric, Christophe Prud'Homme. A successive constraint method with minimal offline constraints for lower bounds of parametric coercivity constant. 2011. ⟨hal-00609212⟩