Deterministic Methods for Stochastic PDEs - Analysis and Implementation
by
Christoph Schwab
ETH Zurich
Coauthors: Marcel Bieri, Radu-Alexandru Todor

We consider the Finite Element Solution of elliptic problems with spatially inhomogeneous random coefficients of finite second moments.
We address fast, FMM-based computation of a Wiener Chaos expansion of Karhunen Loeve (KL) type in infinitely many random variables for given two-point correlation functions of the data in general domains.
Decay estimates for KL Eigenvalues and for the pointwise convergence of the KL expansions are presented.
We present convergence rates and complexity estimates for sparse, ANOVA-type discretization of the random solution, parametrized in the first M KL-Variables of the input data, as the number M of stochastic variables tends to infinity as well as the meshwidth of the spatial Finite Element Discretization tends to zero.
Numerical experiments for Stochastic Galerkin as well as for Collocation Methods in physical dimension 2 and 3 with stochastic dimension M up to 80 are shown.

Date received: June 30, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-62.