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dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorLazarov, Raytcho D.
dc.contributor.authorMoon, Minam
dc.contributor.authorShi, Ke
dc.date.accessioned2015-08-12T09:26:53Z
dc.date.available2015-08-12T09:26:53Z
dc.date.issued2014-10-22
dc.identifier.citationEfendiev, Y., Lazarov, R., Moon, M., & Shi, K. (2015). A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems. Computer Methods in Applied Mechanics and Engineering, 292, 243–256. doi:10.1016/j.cma.2014.09.036
dc.identifier.issn00457825
dc.identifier.doi10.1016/j.cma.2014.09.036
dc.identifier.urihttp://hdl.handle.net/10754/566068
dc.description.abstractWe design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
dc.description.sponsorshipYE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).
dc.publisherElsevier BV
dc.relation.urlhttps://manuscript.elsevier.com/S0045782514003594/pdf/S0045782514003594.pdf
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. 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 [JournalTitle], [[Volume], [Issue], (2014-10-22)] DOI: 10.1016/j.cma.2014.09.036 . © 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsThis file is an open access version redistributed from: https://manuscript.elsevier.com/S0045782514003594/pdf/S0045782514003594.pdf
dc.subjectHybridizable discontinuous Galerkin
dc.subjectMultiscale finite element method
dc.subjectSpectral basis function
dc.titleA spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalComputer Methods in Applied Mechanics and Engineering
dc.rights.embargodate2016-02-02
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, USA
kaust.personEfendiev, Yalchin R.
refterms.dateFOA2020-04-23T11:58:53Z


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