Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Handle URI:
http://hdl.handle.net/10754/563416
Title:
Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients
Authors:
Beck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
In 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.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Stochastic Numerics Research Group
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
Mar-2014
DOI:
10.1016/j.camwa.2013.03.004
Type:
Article
ISSN:
08981221
Sponsors:
The 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.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBeck, Joakimen
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTamellini, Lorenzoen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-03T11:50:55Zen
dc.date.available2015-08-03T11:50:55Zen
dc.date.issued2014-03en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2013.03.004en
dc.identifier.urihttp://hdl.handle.net/10754/563416en
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.en
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.en
dc.publisherElsevier BVen
dc.subjectBest M-terms polynomial approximationen
dc.subjectElliptic PDEs with random dataen
dc.subjectMultivariate polynomial approximationen
dc.subjectStochastic Galerkin methoden
dc.subjectSubexponential convergenceen
dc.subjectUncertainty quantificationen
dc.titleConvergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficientsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.contributor.institutionMOX - Modellistica e Calcolo Scientifico, Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italyen
dc.contributor.institutionCSQI - MATHICSE, Ecole Politechnique Fédérale Lausanne, Station 8, CH 1015, Lausanne, Switzerlanden
kaust.authorTempone, Raulen
kaust.authorBeck, Joakimen
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