Open access
Datum
2002-04Typ
- Report
ETH Bibliographie
yes
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Abstract
We formulate elliptic boundary value problems with stochastic loading in a domain D. We show well-posedness of the problem in stochastic Sobolev spaces and we derive then a deterministic elliptic PDE in DxD for the spatial correlation of the solution. We show well-posedness and regularity results for this PDE in a scale of weighted Sobolev spaces with mixed highest order derivatives. Discretization with sparse tensor products of any hierarchic FE space in D yields optimal asymptotic rates of convergence for the second moments even in the presence of singularities or for spatially completely uncorrelated data. Multilevel preconditioning in DxD allows iterative solution of the discrete equations for the correlation kernel in essentially the same complexity as the solution of the mean field equation. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-a-004339381Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SAM Research ReportBand
Verlag
Seminar for Applied Mathematics, ETH ZurichOrganisationseinheit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
ETH Bibliographie
yes
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