Approximation of Parametric Derivatives by the Empirical Interpolation Method
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Patera_Approximation of parametric.pdf
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Author(s)
Grepl, Martin A.
Patera, Anthony T.
Ronquist, Einar M.
Eftang, Jens L.
Date Issued
June 2012
Journal
Foundations of Computational Mathematics
Publisher
Springer-Verlag
Citation
Eftang, Jens L., Martin A. Grepl, Anthony T. Patera, and Einar M. Rønquist. Approximation of Parametric Derivatives by the Empirical Interpolation Method. Foundations of Computational Mathematics (June 19, 2012).
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Author's final manuscript
Abstract
We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory.
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/10.1007/s10208-012-9125-9
