A Monotonic Evaluation of Lower Bounds for Inf-Sup Stability Constants in the Frame of Reduced Basis Approximations

Yanlai Chen, Jan Sickmann Hesthaven, Yvon Maday and
Jerónimo Rodríguez

june, 2008

Publication type:

Paper in peer-reviewed journals

Journal:

C. R. Acad. Sci. Paris, Ser. I, vol. 346 (23-24), pp. 1295--1300

DOI:

10.1016/j.crma.2008.10.012

HAL:

hal-00873076

Keywords :

A posteriori error estimation, inf-sup stability constant, reduced basis method, Succesive constraint method, non coercive problems

Abstract:

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 in [2] by providing a monotonic version of this algorithm that leads to both more stable evaluations and fewer oﬄine computations.

Abstract (translation) :

Un ingrŽedient fondamental de l�analyse a posteriori pour l�approximation par mŽethode par bases rŽeduites de probl`emes coercifs ou non coercifs est la dŽeﬁnition de bornes ﬁables pour la constante de coercivitŽe ou la constante inf-sup. Dans cette Note, nous gŽenŽeralisons et amŽeliorons la mŽethode d�optimisation linŽeaire de contraintes suc- cessives prŽesentŽees dans [2], en proposant une version monotone de cet algorithme qui conduit `a la fois `a des Ževaluations plus stables et un nombre rŽeduit de calculs hors ligne.

BibTeX:

@article{Che-Hes-Mad-Rod-2008,
    author={Yanlai Chen and Jan Sickmann Hesthaven and Yvon Maday and 
           Jerónimo Rodríguez },
    title={A Monotonic Evaluation of Lower Bounds for Inf-Sup Stability 
           Constants in the Frame of Reduced Basis Approximations },
    doi={10.1016/j.crma.2008.10.012 },
    journal={C. R. Acad. Sci. Paris, Ser. I },
    year={2008 },
    month={6},
    volume={346 (23-24) },
    pages={1295--1300},
}