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dc.contributor.author
Hoang, V. H.
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2017-06-09T16:48:43Z
dc.date.available
2017-06-09T16:48:43Z
dc.date.issued
2011-02
dc.identifier.uri
http://hdl.handle.net/20.500.11850/40058
dc.description.abstract
A class of second order, elliptic PDEs in divergence form with stochastic and anisotropic conductivity coefficients and $n$ known, separated microscopic length scales $\epsilon_i$, $i=1,...,n$ in a bounded domain $D\subset \IR^d$ is considered. Neither stationarity nor ergodicity of these coefficients is assumed. Sufficient conditions are given for the random solution to converge $\IP$-a.s, as $\epsilon_i\rightarrow 0$, to a stochastic, elliptic one-scale limit problem in a tensorized domain of dimension $(n+1)d$. It is shown that this stochastic limit problem admits best $N$-term "polynomial chaos" type approximations which converge at a rate $\sigma>0$ that is determined by the summability of the random inputs' Karhúnen-Loève expansion. The convergence of the polynomial chaos expansion is shown to hold $\IP$-a.s. and uniformly with respect to the scale parameters $\epsilon_i$. Regularity results for the stochastic, one-scale limiting problem are established. An error bound for the approximation of the random solution at finite, positive values of the scale parameters $\epsilon_i$ is established in the case of two scales, and in the case of $n>2$ scales convergence is shown, albeit without giving a convergence rate in this case.
dc.language.iso
en
dc.publisher
Seminar für Angewandte Mathematik, ETH
dc.title
Analytic regularity and polynomial approximation of stochastic, parametric elliptic multiscale PDEs
dc.type
Report
ethz.journal.title
Research reports
ethz.journal.issue
2011/07
ethz.journal.abbreviated
Res. rep.- Natl. Geogr. Soc.
ethz.notes
Revised July 2011.
ethz.publication.place
Zürich
ethz.publication.status
unpublished
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.identifier.url
http://www.sam.math.ethz.ch/reports/2011/07
ethz.date.deposited
2017-06-09T16:48:46Z
ethz.source
ECIT
ethz.identifier.importid
imp59364e8f400a384961
ethz.ecitpid
pub:67176
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-18T08:53:14Z
ethz.rosetta.lastUpdated
2018-10-01T14:01:17Z
ethz.rosetta.versionExported
true
ethz.COinS
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