Generalized multiscale finite element method. Symmetric interior penalty coupling

Handle URI:
http://hdl.handle.net/10754/563114
Title:
Generalized multiscale finite element method. Symmetric interior penalty coupling
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.
Abstract:
Motivated 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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Dec-2013
DOI:
10.1016/j.jcp.2013.07.028
ARXIV:
arXiv:1302.7071
Type:
Article
ISSN:
00219991
Sponsors:
Y.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).
Additional Links:
http://arxiv.org/abs/arXiv:1302.7071v1
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, Juanen
dc.contributor.authorLazarov, Raytcho D.en
dc.contributor.authorMoon, M.en
dc.contributor.authorSarkis, Marcus V.en
dc.date.accessioned2015-08-03T11:36:06Zen
dc.date.available2015-08-03T11:36:06Zen
dc.date.issued2013-12en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2013.07.028en
dc.identifier.urihttp://hdl.handle.net/10754/563114en
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.en
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).en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1302.7071v1en
dc.subjectDiscontinuous Galerkinen
dc.subjectMultiscale finite element methoden
dc.subjectSnapshot spacesen
dc.subjectUpscalingen
dc.titleGeneralized multiscale finite element method. Symmetric interior penalty couplingen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, United Statesen
dc.contributor.institutionDepartamento de Matemáticas, Universidad Nacional de Colombia, Carrera 45 No. 26-85, Edificio Uriel Gutierréz, Bogotá D.C., Colombiaen
dc.contributor.institutionMathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, United Statesen
dc.contributor.institutionInstituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, Brazilen
dc.identifier.arxividarXiv:1302.7071en
kaust.authorEfendiev, Yalchin R.en
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