330 RWTH Publication No: 47330        2011        IGPM330.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 approximation 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 consider 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)