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dc.contributor.authorChung, Eric T.
dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorLeung, Wing Tat
dc.date.accessioned2015-09-13T12:20:14Z
dc.date.available2015-09-13T12:20:14Z
dc.date.issued2015-09-08
dc.identifier.citationResidual-driven online generalized multiscale finite element methods 2015 Journal of Computational Physics
dc.identifier.issn00219991
dc.identifier.doi10.1016/j.jcp.2015.07.068
dc.identifier.urihttp://hdl.handle.net/10754/577236
dc.description.abstractThe construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast. We note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects. Using the residual information, we can incorporate the distant information provided the offline approximation satisfies certain properties. In the paper, theoretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large (in terms of the dimension) such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the contrast. We discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0021999115005744
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, 8 September 2015. DOI: 10.1016/j.jcp.2015.07.068
dc.subjectMultiscale finite element method
dc.subjectLocal model reduction
dc.subjectAdaptivity
dc.subjectOnline basis construction
dc.titleResidual-driven online generalized multiscale finite element methods
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalJournal of Computational Physics
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, TX, USA
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxivid1501.04565
kaust.personEfendiev, Yalchin R.
refterms.dateFOA2017-09-08T00:00:00Z
dc.date.published-online2015-09-08
dc.date.published-print2015-12


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