A priori convergence of the Greedy algorithm for the parametrized reduced basis method
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Patera_A priori convergence.pdf
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Author(s)
Buffa, Annalisa
Maday, Yvon
Patera, Anthony T.
Prud’homme, Christophe
Turinici, Gabriel
Date Issued
January 2012
Journal
ESAIM: Mathematical Modelling and Numerical Analysis
Publisher
Cambridge University Press
Citation
Buffa, Annalisa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, and Gabriel Turinici. A Priori Convergence of the Greedy Algorithm for the Parametrized Reduced Basis Method. ESAIM: Mathematical Modelling and Numerical Analysis 46, no. 3 (May 11, 2012): 595-603.
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1051/m2an/2011056
