326	RWTH Publication No: 47321        2011        IGPM326.pdf
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)