A Posteriori Error Bounds for the Empirical Interpolation Method
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Patera_A posteriori.pdf
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Author(s)
Eftang, Jens L.
Grepl, Martin A.
Patera, Anthony T.
Alternative Title
A posteriori error bounds for the empirical interpolation method Un estimateur a posteriori d'erreur pour la méthode d'interpolation empirique
Date Issued
March 2010
Journal
Comptes Rendus Mathematique
Publisher
Académie des sciences. Published by Elsevier Masson SAS
Citation
Eftang, Jens L., Martin A. Grepl, and Anthony T. Patera. “A Posteriori Error Bounds For the Empirical Interpolation Method.” Comptes Rendus Mathematique 348.9-10 (2010) : 575-579.
Version
Author's final manuscript
Abstract
We present rigorous a posteriori error bounds for the Empirical Interpolation Method (EIM). The essential ingredients are (i) analytical upper bounds for the parametric derivatives of the function to be approximated, (ii) the EIM “Lebesgue constant,” and (iii) information concerning the EIM approximation error at a finite set of points in parameter space. The bound is computed “off-line” and is valid over the entire parameter domain; it is thus readily employed in (say) the “on-line” reduced basis context. We present numerical results that confirm the validity of our approach.
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/10.1016/j.crma.2010.03.004
