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dc.contributor.authorBeck, Joakim
dc.contributor.authorNobile, Fabio
dc.contributor.authorTamellini, Lorenzo
dc.contributor.authorTempone, Raul
dc.date.accessioned2015-08-03T11:50:55Z
dc.date.available2015-08-03T11:50:55Z
dc.date.issued2014-03
dc.identifier.issn08981221
dc.identifier.doi10.1016/j.camwa.2013.03.004
dc.identifier.urihttp://hdl.handle.net/10754/563416
dc.description.abstractIn this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.
dc.description.sponsorshipThe authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) AEA project "Predictability and Uncertainty Quantification for Models of Porous Media" is also acknowledged. The second and third authors have been supported by the Italian grant FIRB-IDEAS (Project n. RBID08223Z) "Advanced numerical techniques for uncertainty quantification in engineering and life science problems". The fourth author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
dc.publisherElsevier BV
dc.subjectBest M-terms polynomial approximation
dc.subjectElliptic PDEs with random data
dc.subjectMultivariate polynomial approximation
dc.subjectStochastic Galerkin method
dc.subjectSubexponential convergence
dc.subjectUncertainty quantification
dc.titleConvergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalComputers & Mathematics with Applications
dc.contributor.institutionMOX - Modellistica e Calcolo Scientifico, Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy
dc.contributor.institutionCSQI - MATHICSE, Ecole Politechnique Fédérale Lausanne, Station 8, CH 1015, Lausanne, Switzerland
kaust.personTempone, Raul
kaust.personBeck, Joakim


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