Volume 46, Number 3, May-June 2012Special volume in honor of Professor David Gottlieb
|Page(s)||595 - 603|
|Published online||11 January 2012|
A priori convergence of the Greedy algorithm for the parametrized reduced basis method
Instituto di Matematica Applicata e Tecnologie Informatiche –
CNR, Via Ferrata 1,
2 UPMC Univ Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
3 Division of Applied Mathematics, Brown University, Providence, RI, USA
4 Massachusetts Institute of Technology, Department of Mechanical Engineering, Room 3-266, 77 Mass. Ave., Cambridge, 02139-4307 MA, USA
5 Université de Grenoble 1-Joseph Fourier, Laboratoire Jean Kuntzmann, 51 rue des Mathèmatiques, BP 53, 38041 Grenoble Cedex 9, France
6 Université Paris Dauphine, CEREMADE, Place du Marechal de Lattre de Tassigny, 75016 Paris, France
Received: 9 November 2009
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.
Mathematics Subject Classification: 41A45 / 41A65 / 65N15
Key words: Greedy algorithm / reduced basis approximations / a priori analysis / best fit analysis
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.