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

Oleg P. Iliev; Raytcho D. Lazarov; Joerg Willems

doi:10.1007/978-3-642-12535-5_2

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

Oleg P. Iliev, Raytcho D. Lazarov, Joerg Willems

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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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.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science
Publisher	Springer Nature
Pages	14-25
Number of pages	12
ISBN (Print)	9783642125348
DOIs	https://doi.org/10.1007/978-3-642-12535-5_2
State	Published - 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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Cite this

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title = "Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman{\textquoteright}s Equations",

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. {\textcopyright} 2010 Springer-Verlag Berlin Heidelberg.",

author = "Iliev, {Oleg P.} and Lazarov, {Raytcho D.} and Joerg Willems",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/978-3-642-12535-5_2",

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AU - Lazarov, Raytcho D.

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N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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ER -

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

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