Sparse finite elements for stochastic elliptic problems - higher order moments
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2003-06
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Report
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Abstract
We define the higher order moments associated to the stochastic solution of an elliptic BVP in D \subset Rd with stochastic source terms and boundary data. We prove that the k-th moment (or k-point correlation function) of the random solution solves a deterministic problem in Dk \subset Rdk. We discuss well-posedness and regularity in scales of Sobolev spaces with bounded mixed derivatives. We discretize this deterministic k-th moment problem using sparse tensor product FE-spaces and, exploiting a spline wavelet basis, we propose an algorithm of (up to logarithmic terms) the same accuracy and complexity as a multigrid finite element method for the mean field problem in D.
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published
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2003-04
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Seminar for Applied Mathematics, ETH Zurich
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Subject
stochastic PDE; sparse grids; finite elements; wavelets
Organisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
03435 - Schwab, Christoph / Schwab, Christoph