330 | IGPM330.pdf September 2011 |

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) |