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dc.contributor.authorChung, Eric T.
dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorLeung, Wing Tat
dc.date.accessioned2017-04-13T11:50:59Z
dc.date.available2017-04-13T11:50:59Z
dc.date.issued2017-02-07
dc.identifier.citationChung ET, Efendiev Y, Leung WT (2017) An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media. Communications in Computational Physics 21: 401–422. Available: http://dx.doi.org/10.4208/cicp.230815.090516a.
dc.identifier.issn1815-2406
dc.identifier.issn1991-7120
dc.identifier.doi10.4208/cicp.230815.090516a
dc.identifier.urihttp://hdl.handle.net/10754/623175
dc.description.abstractOffline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.
dc.description.sponsorshipThis research is partially supported by the Hong Kong RGC General Research Fund (Project number: 400813). YE would like to thank the partial support from NSF 1620318, the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics programunderAwardNumberDE-FG02-13ER26165 and National Priorities Research Program grant 7-1482-1278 from the Qatar National Research Fund
dc.publisherGlobal Science Press
dc.relation.urlhttps://www.cambridge.org/core/journals/communications-in-computational-physics/article/div-classtitlean-online-generalized-multiscale-discontinuous-galerkin-method-gmsdgm-for-flows-in-heterogeneous-mediadiv/418FDB6625A730285F94991DC65E042F
dc.subjectdiscontinuous Galerkin method
dc.subjectheterogeneous media
dc.subjectMultiscale method
dc.subjectonline basis functions
dc.titleAn Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalCommunications in Computational Physics
dc.contributor.institutionDepartment of Mathematics, Chinese University of Hong Kong, Hong Kong
dc.contributor.institutionDepartment of Mathematics, Texas AandM University, College Station, TX, 77843-3368, United States
dc.identifier.arxivid1504.04417
kaust.personEfendiev, Yalchin R.
dc.date.published-online2017-02-07
dc.date.published-print2017-02


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