Show simple item record

dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorGalvis, Juan
dc.contributor.authorLazarov, Raytcho D.
dc.contributor.authorMoon, M.
dc.contributor.authorSarkis, Marcus V.
dc.date.accessioned2015-08-03T11:36:06Z
dc.date.available2015-08-03T11:36:06Z
dc.date.issued2013-12
dc.identifier.issn00219991
dc.identifier.doi10.1016/j.jcp.2013.07.028
dc.identifier.urihttp://hdl.handle.net/10754/563114
dc.description.abstractMotivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
dc.description.sponsorshipY.E.'s work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).J. Galvis would like to acknowledge partial support from DOE. R. Lazarov's research was supported in parts by NSF (DMS 1016525).
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/abs/arXiv:1302.7071v1
dc.subjectDiscontinuous Galerkin
dc.subjectMultiscale finite element method
dc.subjectSnapshot spaces
dc.subjectUpscaling
dc.titleGeneralized multiscale finite element method. Symmetric interior penalty coupling
dc.typeArticle
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalJournal of Computational Physics
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, United States
dc.contributor.institutionDepartamento de Matemáticas, Universidad Nacional de Colombia, Carrera 45 No. 26-85, Edificio Uriel Gutierréz, Bogotá D.C., Colombia
dc.contributor.institutionMathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, United States
dc.contributor.institutionInstituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, Brazil
dc.identifier.arxividarXiv:1302.7071
kaust.personEfendiev, Yalchin R.


This item appears in the following Collection(s)

Show simple item record