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dc.contributor.authorHall, Eric Joseph
dc.contributor.authorHoel, Håkon
dc.contributor.authorSandberg, Mattias
dc.contributor.authorSzepessy, Anders
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-01-08T13:05:38Z
dc.date.available2017-01-08T13:05:38Z
dc.date.issued2016-12-08
dc.identifier.citationHall EJ, Hoel H, Sandberg M, Szepessy A, Tempone R (2016) Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data. SIAM Journal on Scientific Computing 38: A3773–A3807. Available: http://dx.doi.org/10.1137/15M1044266.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/15M1044266
dc.identifier.urihttp://hdl.handle.net/10754/622637
dc.description.abstractWe derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.
dc.description.sponsorshipThis research was supported by Swedish Research Council grant VR-621-2014-4776 and the Swedish e-Science Research Center. It was carried out while the first author was a Goran Gustafsson postdoctoral fellow at KTH Royal Institute of Technology. The second author was supported by Norges Forskningsrad, research project 214495 LIQCRY. The fifth author is a member of the KAUST Strategic Research Initiative, Center for Uncertainty Quantification in Computational Sciences and Engineering, and was supported by the KAUST CRG3 Award ref. 2281.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1044266
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.subjectA posteriori error
dc.subjectElliptic PDE
dc.subjectGalerkin error
dc.subjectLognormal
dc.subjectMonte Carlo methods
dc.subjectQuadrature error
dc.subjectRandom PDE
dc.titleComputable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 10030, United States
dc.contributor.institutionDepartment of Mathematics, University of Oslo, Oslo, 0316, Norway
dc.contributor.institutionDepartment of Mathematics, KTH Royal Institute of Technology, Stockholm, 100 44, Sweden
dc.identifier.arxividarXiv:1510.02708
kaust.personTempone, Raul
kaust.grant.numberCRG3 Award ref. 2281
refterms.dateFOA2018-06-13T15:39:27Z
dc.date.published-online2016-12-08
dc.date.published-print2016-01


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