Mixed Generalized Multiscale Finite Element Methods and Applications

Handle URI:
http://hdl.handle.net/10754/347292
Title:
Mixed Generalized Multiscale Finite Element Methods and Applications
Authors:
Chung, Eric T.; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Lee, Chak Shing
Abstract:
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Mixed Generalized Multiscale Finite Element Methods and Applications 2015, 13 (1):338 Multiscale Modeling & Simulation
Publisher:
Society for Industrial and Applied Mathematics
Journal:
Multiscale Modeling & Simulation
Issue Date:
3-Mar-2015
DOI:
10.1137/140970574
Type:
Article
ISSN:
1540-3459; 1540-3467
Additional Links:
http://epubs.siam.org/doi/10.1137/140970574
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorChung, Eric T.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorLee, Chak Shingen
dc.date.accessioned2015-03-30T12:57:13Zen
dc.date.available2015-03-30T12:57:13Zen
dc.date.issued2015-03-03en
dc.identifier.citationMixed Generalized Multiscale Finite Element Methods and Applications 2015, 13 (1):338 Multiscale Modeling & Simulationen
dc.identifier.issn1540-3459en
dc.identifier.issn1540-3467en
dc.identifier.doi10.1137/140970574en
dc.identifier.urihttp://hdl.handle.net/10754/347292en
dc.description.abstractIn this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.en
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140970574en
dc.rightsArchived with thanks to Multiscale Modeling & Simulation. © 2015, Society for Industrial and Applied Mathematicsen
dc.titleMixed Generalized Multiscale Finite Element Methods and Applicationsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalMultiscale Modeling & Simulationen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SARen
dc.contributor.institutionDepartment of Mathematics & Institute for Scientific Computation (ISC), Texas A&M Uni- versity, College Station, TXen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorEfendiev, Yalchin R.en
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