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dc.contributor.authorBuffa, Annalisa
dc.contributor.authorMaday, Yvon
dc.contributor.authorPatera, Anthony T.
dc.contributor.authorPrud'Homme, Christophe
HAL ID: 1108
ORCID: 0000-0003-2287-2961
dc.contributor.authorTurinici, Gabriel
HAL ID: 16
ORCID: 0000-0003-2713-006X
dc.subjectreduced basis approximationsen
dc.subjectGreedy algorithmen
dc.subjecta priori analysisen
dc.subjectbest fit analysisen
dc.titleA priori convergence of the Greedy algorithm for the parametrized reduced basis methoden
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire Jacques-Louis Lions (LJLL) CNRS : UMR7598 – Université Paris VI - Pierre et Marie Curie;France
dc.contributor.editoruniversityotherDepartment of Mechanical Engineering (MIT-MECHE) Massachussetts Institute of Technology (MIT);États-Unis
dc.contributor.editoruniversityotherLaboratoire Jean Kuntzmann (LJK) CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble;France
dc.contributor.editoruniversityotherInstitut de Recherche Mathématique Avancée (IRMA) CNRS : UMR7501 – Université de Strasbourg;France
dc.contributor.editoruniversityotherDipartimento di Matematica - Università di Pavia Università degli studi di Pavia;Italie
dc.description.abstractenThe 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.en
dc.relation.isversionofjnlnameModélisation mathématique et analyse numérique
dc.relation.isversionofjnlpublisherEDP Sciencesen

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