Schwab, Christoph and Suli, Endre (2011) Adaptive Galerkin approximation algorithms for partial differential equations in infinite dimensions. Technical Report. Unspecified. (Submitted)

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Abstract
Spacetime variational formulations of infinitedimensional FokkerPlanck (FP) and OrnsteinUhlenbeck (OU) equations for functions on a separable Hilbert space are developed. The wellposedness of these equations in the Hilbert space of functions on , which are squareintegrable with respect to a Gaussian measure on , is proved. Specifically, for the infinitedimensional FP equation, adaptive spacetime Galerkin discretizations, based on a tensorized Riesz basis, built from biorthogonal piecewise polynomial wavelet bases in time and the Hermite polynomial chaos in the WienerItô decomposition of , are introduced and are shown to converge quasioptimally with respect to the nonlinear, best term approximation benchmark. As a consequence, the proposed adaptive Galerkin solution algorithms perform quasioptimally with respect to the best term approximation in the finitedimensional case, in particular. All constants in our error and complexity bounds are shown to be independent of the number of "active" coordinates identified by the proposed adaptive Galerkin approximation algorithms.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1452 
Deposited By:  Lotti Ekert 
Deposited On:  02 Dec 2011 08:59 
Last Modified:  29 May 2015 19:09 
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