Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

Handle URI:
http://hdl.handle.net/10754/597991
Title:
Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations
Authors:
Iliev, Oleg P.; Lazarov, Raytcho D.; Willems, Joerg
Abstract:
We present a two-scale finite element method for solving Brinkman's equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy's equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.
Citation:
Iliev OP, Lazarov RD, Willems J (2010) Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations. Lecture Notes in Computer Science: 14–25. Available: http://dx.doi.org/10.1007/978-3-642-12535-5_2.
Publisher:
Springer Science + Business Media
Journal:
Lecture Notes in Computer Science
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
2010
DOI:
10.1007/978-3-642-12535-5_2
Type:
Book Chapter
ISSN:
0302-9743; 1611-3349
Sponsors:
The research of O. Iliev was supported by DAAD-PPPD/07/10578 and award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). R. Lazarov has been supported by award KUS-C1-016-04, made by KAUST, by NSF Grant DMS-0713829, and by the European School for Industrial Mathematics (ESIM) sponsored by the Eras-mus Mundus program of the EU. J. Willems was supported by DAAD-PPPD/07/10578, NSF Grant DMS-0713829, and the Studienstiftung des deutschen Volkes (German National Academic Foundation). Part of the research was per-formed during the visit of O. Iliev to Texas A&M University. The hospitality of the Institute of Applied Mathematics and Computational Science, funded by KAUST, and the Institute for Scientific Computing are gratefully acknowledged. The authors express sincere thanks to Dr. Yalchin Efendiev for his valuable comments and numerous discussion on the subject of this paper.
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Full metadata record

DC FieldValue Language
dc.contributor.authorIliev, Oleg P.en
dc.contributor.authorLazarov, Raytcho D.en
dc.contributor.authorWillems, Joergen
dc.date.accessioned2016-02-25T13:10:30Zen
dc.date.available2016-02-25T13:10:30Zen
dc.date.issued2010en
dc.identifier.citationIliev OP, Lazarov RD, Willems J (2010) Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations. Lecture Notes in Computer Science: 14–25. Available: http://dx.doi.org/10.1007/978-3-642-12535-5_2.en
dc.identifier.issn0302-9743en
dc.identifier.issn1611-3349en
dc.identifier.doi10.1007/978-3-642-12535-5_2en
dc.identifier.urihttp://hdl.handle.net/10754/597991en
dc.description.abstractWe present a two-scale finite element method for solving Brinkman's equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy's equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThe research of O. Iliev was supported by DAAD-PPPD/07/10578 and award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). R. Lazarov has been supported by award KUS-C1-016-04, made by KAUST, by NSF Grant DMS-0713829, and by the European School for Industrial Mathematics (ESIM) sponsored by the Eras-mus Mundus program of the EU. J. Willems was supported by DAAD-PPPD/07/10578, NSF Grant DMS-0713829, and the Studienstiftung des deutschen Volkes (German National Academic Foundation). Part of the research was per-formed during the visit of O. Iliev to Texas A&M University. The hospitality of the Institute of Applied Mathematics and Computational Science, funded by KAUST, and the Institute for Scientific Computing are gratefully acknowledged. The authors express sincere thanks to Dr. Yalchin Efendiev for his valuable comments and numerous discussion on the subject of this paper.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectBrinkman's equationsen
dc.subjectFlow in heterogeneous porous mediaen
dc.subjectMixed FEMen
dc.subjectNumerical upscalingen
dc.subjectSubgrid approximationen
dc.titleDiscontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equationsen
dc.typeBook Chapteren
dc.identifier.journalLecture Notes in Computer Scienceen
dc.contributor.institutionFraunhofer-Institut fur Techno- und Wirtschaftsmathematk, Kaiserslautern, Germanyen
dc.contributor.institutionInstitute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgariaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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