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Preprint-No.: <   330   >   Published in: September 2011   PDF-File: IGPM330_k.pdf
Title:Approximation of Parametric Derivatives by the Empirical Interpolation Method
Authors:Jens L. Eftang, Martin A. Grepl, Anthony T. Patera, Einar M. Rønquist
Abstract:
We introduce a general a priori convergence result for the approx- imation of parametric derivatives of parametrized functions. We show that for a given approximation scheme the approximations of parametric derivatives of a given parametrized function are convergent provided that the approximation of the function itself is convergent. The assumptions on the approximation scheme are rather weak; for example we may con- sider both projection-based and interpolation-based approximation. We present numerical results with one particular interpolation scheme — the Empirical Interpolation Method — to confirm the validity of the general theory.
Keywords: function approximation; a priori convergence; Empirical Interpolation Method; parametric derivatives; sensitivity derivatives
DOI: 10.1007/s10208-012-9125-9
Publication:Foundations of computational mathematics
13(5), 763-787 (2013)