Stochastic Galerkin approximation of operator equations with infinite dimensional noise
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Author
Date
2011-02Type
- Report
ETH Bibliography
yes
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Abstract
It is common practice in the study of stochastic Galerkin methods for boundary value problems depending on random fields to truncate a series representation of this field prior to the Galerkin discretization. We show that this is unnecessary; the projection onto a finite dimensional subspace automatically replaces the infinite series expansion by a suitable partial sum. We construct tensor product polynomial bases on infinite dimensional parameter domains, and use these to recast a random boundary value problem as a countably infinite system of deterministic equations. The stochastic Galerkin method can be interpreted as a standard finite element discretization of a finite section of this infinite system. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010388303Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
03435 - Schwab, Christoph / Schwab, Christoph
Funding
247277 - Automated Urban Parking and Driving (EC)
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ETH Bibliography
yes
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