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dc.contributor.authorChung, Eric T.
dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorLeung, Wing Tat
dc.date.accessioned2019-03-11T07:10:35Z
dc.date.available2019-03-11T07:10:35Z
dc.date.issued2018-08-07
dc.identifier.citationChung ET, Efendiev Y, Leung WT (2018) An Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems. Multiscale Modeling & Simulation 16: 1227–1257. Available: http://dx.doi.org/10.1137/140986189.
dc.identifier.issn1540-3459
dc.identifier.issn1540-3467
dc.identifier.doi10.1137/140986189
dc.identifier.urihttp://hdl.handle.net/10754/631503
dc.description.abstractIn this paper, we develop an adaptive generalized multiscale discontinuous Galerkin method (GMsDGM) for a class of high-contrast flow problems and derive a priori and a posteriori error estimates for the method. Based on the a posteriori error estimator, we develop an adaptive enrichment algorithm for our GMsDGM and prove its convergence. The adaptive enrichment algorithm gives an automatic way to enrich the approximation space in regions where the solution requires more basis functions, which are shown to perform well compared with a uniform enrichment. We also discuss an approach that adaptively selects multiscale basis functions by correlating the residual to multiscale basis functions (cf. [S. S. Chen, D. L. Donoho, and M. A. Saunders, SIAM Rev., 43 (2001), pp. 129-159]). The proposed error indicators are L-based and can be inexpensively computed, which makes our approach efficient. Numerical results are presented that demonstrate the robustness of the proposed error indicators.
dc.description.sponsorshipThe first author was partially supported by the Hong Kong RGC General Research Fund (project 400813) and CUHK Direct Grant for Research 2013/14.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/140986189
dc.rightsArchived with thanks to Multiscale Modeling & Simulation
dc.subjectAdaptivity
dc.subjectDiscontinuous Galerkin method
dc.subjectHigh-contrast flow
dc.subjectModel reduction
dc.subjectMultiscale finite element method
dc.titleAn Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalMultiscale Modeling & Simulation
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics, Chinese University of Hong Kong, Hong Kong, , Hong Kong
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX, 77840, , United States
kaust.personEfendiev, Yalchin R.
refterms.dateFOA2019-03-11T12:22:47Z


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