Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Handle URI:
http://hdl.handle.net/10754/594717
Title:
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
Authors:
Beck, Joakim; Nobile, F.; Tamellini, L.; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.
KAUST Department:
Applied Mathematics and Computational Science Program
Citation:
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients 2011, 33:10 ESAIM: Proceedings
Publisher:
EDP Sciences
Journal:
ESAIM: Proceedings
Issue Date:
22-Dec-2011
DOI:
10.1051/proc/201133002
Type:
Conference Paper
ISSN:
1270-900X
Additional Links:
http://www.esaim-proc.org/10.1051/proc/201133002
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorBeck, Joakimen
dc.contributor.authorNobile, F.en
dc.contributor.authorTamellini, L.en
dc.contributor.authorTempone, Raulen
dc.date.accessioned2016-01-24T07:17:36Zen
dc.date.available2016-01-24T07:17:36Zen
dc.date.issued2011-12-22en
dc.identifier.citationImplementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients 2011, 33:10 ESAIM: Proceedingsen
dc.identifier.issn1270-900Xen
dc.identifier.doi10.1051/proc/201133002en
dc.identifier.urihttp://hdl.handle.net/10754/594717en
dc.description.abstractIn this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.en
dc.language.isoenen
dc.publisherEDP Sciencesen
dc.relation.urlhttp://www.esaim-proc.org/10.1051/proc/201133002en
dc.rightsArchived with thanks to ESAIM: Proceedingsen
dc.subjectUncertainty Quantificationen
dc.subjectPDEs with random dataen
dc.subjectelliptic equationsen
dc.subjectmultivariate polynomial approximationen
dc.subjectBest M-Terms approximationen
dc.subjectStochastic Galerkin methodsen
dc.subjectSmolyak approximationen
dc.subjectSparse grids, Stochastic Collocation methodsen
dc.titleImplementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficientsen
dc.typeConference Paperen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalESAIM: Proceedingsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionMOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Italyen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorBeck, Joakimen
kaust.authorTempone, Raulen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.