A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud'Homme, Christophe; Turinici, Gabriel

Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud'Homme, Christophe; Turinici, Gabriel (2012), A priori convergence of the Greedy algorithm for the parametrized reduced basis method, Modélisation mathématique et analyse numérique, 46, 3, p. 595-603. http://dx.doi.org/10.1051/m2an/2011056

Type

Article accepté pour publication ou publié

Date

2012

Nom de la revue

Modélisation mathématique et analyse numérique

Volume

Numéro

Éditeur

EDP Sciences

Pages

595-603

Résumé (EN)

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the "reduced basis". The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that three greedy algorithms converge; the last algorithm, based on the use of an a posteriori estimator, is the approach actually employed in the calculations.

Mots-clés

reduced basis approximations; Greedy algorithm; a priori analysis; best fit analysis