Analyse numérique/Numerical Analysis A Successive Constraint Linear Optimization Method for Lower Bounds of Parametric Coercivity and Inf-Sup Stability Constants
نویسنده
چکیده
We present an approach to the construction of lower bounds for the coercivity and inf-sup stability constants required in a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. The method, based on an Offline-Online strategy relevant in the reduced basis many-query and real-time context, reduces the Online calculation to a small Linear Program: the objective is a parametric expansion of the underlying Rayleigh quotient; the constraints reflect stability information at optimally selected parameter points. Numerical results are presented for an (coercive) elasticity problem and an (non-coercive) acoustics Helmholtz problem. To cite this article : D.B.P. Huynh, G. Rozza, S. Sen, A.T. Patera, C. R. Acad. Sci.Paris, Ser. xxxx (2007). Une Méthode d’Optimisation Linéaire de Constraintes Successives pour les Bournes Inférieures des Constantes de Stabilité Paramètrique Coercive et Inf-Sup
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