|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|
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|
|Publication:||Foundations of computational mathematics |
13(5), 763-787 (2013)