A Posteriori Error Bounds for the Empirical Interpolation Method

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 "offline" and is valid over the entire parameter domain; it is thus readily employed in (say) the "online" reduced basis context. We present numerical results that confirm the validity of our approach.

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Document Details

Document Type
Technical Report
Publication Date
Mar 18, 2010
Accession Number
ADA557554

Entities

People

  • Anthony T. Patera
  • Jens L. Eftang
  • Martin A. Grepl

Organizations

  • Massachusetts Institute of Technology

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  • Coefficients
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  • Differential Equations
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  • Interpolation
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