326 IGPM326.pdf        May 2011
TITLE Certified Reduced Basis Methods for Nonaffine Linear Time-Varying Partial Differential Equations
AUTHORS Martin A. Grepl
ABSTRACT We present reduced basis approximations and associated a posteriori error bounds for nonaffine linear time-varying parabolic partial differential equations. We employ the Empirical Interpolation Method in order to construct “affine” coefficient-function approximations of the “nonaffine” parametrized functions. To this end, we extend previous work on time-invariant functions to time-varying functions and introduce a new sampling approach to generate the function approximation space for the latter case. Our a posteriori error bounds take both error contributions explicitly into account - the error introduced by the reduced basis approximation and the error induced by the coefficient function interpolation. We present an efficient offline-online computational procedure for the calculation of the reduced basis approximation and associated error bound. Numerical results are presented to confirm and test our approach.
KEYWORDS Reduced basis methods, parabolic PDEs, parameter-dependent systems, a posteriori error estimation, time-varying problems
DOI 10.1142/S0218202511500151
PUBLICATION Mathematical models & methods in applied sciences
M 3 AS 22(3), 1150015, 40 S. (2012)