A strongly conservative finite element method for the coupling of Stokes and Darcy flow

G. Kanschat; B. Rivière

doi:10.1016/j.jcp.2010.04.021

A strongly conservative finite element method for the coupling of Stokes and Darcy flow

G. Kanschat, B. Rivière

Research output: Contribution to journal › Article › peer-review

136 Scopus citations

Abstract

We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. © 2010 Elsevier Inc.

Original language	English (US)
Pages (from-to)	5933-5943
Number of pages	11
Journal	Journal of Computational Physics
Volume	229
Issue number	17
DOIs	https://doi.org/10.1016/j.jcp.2010.04.021
State	Published - Aug 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Supported in part by the National Science Foundation through Grant Nos DMS-0713829 and DMS-0810387 and by the King Abdullah University of Science and Technology (KAUST) through Award No KUS-CI-016-04Supported in part by the National Science Foundation through Grant No DMS-0810422
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.jcp.2010.04.021

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title = "A strongly conservative finite element method for the coupling of Stokes and Darcy flow",

abstract = "We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. {\textcopyright} 2010 Elsevier Inc.",

author = "G. Kanschat and B. Rivi{\`e}re",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-CI-016-04 Acknowledgements: Supported in part by the National Science Foundation through Grant Nos DMS-0713829 and DMS-0810387 and by the King Abdullah University of Science and Technology (KAUST) through Award No KUS-CI-016-04Supported in part by the National Science Foundation through Grant No DMS-0810422 This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2010",

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doi = "10.1016/j.jcp.2010.04.021",

language = "English (US)",

volume = "229",

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journal = "Journal of Computational Physics",

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T1 - A strongly conservative finite element method for the coupling of Stokes and Darcy flow

AU - Kanschat, G.

AU - Rivière, B.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-CI-016-04 Acknowledgements: Supported in part by the National Science Foundation through Grant Nos DMS-0713829 and DMS-0810387 and by the King Abdullah University of Science and Technology (KAUST) through Award No KUS-CI-016-04Supported in part by the National Science Foundation through Grant No DMS-0810422 This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/8

Y1 - 2010/8

N2 - We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. © 2010 Elsevier Inc.

AB - We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. © 2010 Elsevier Inc.

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DO - 10.1016/j.jcp.2010.04.021

M3 - Article

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VL - 229

SP - 5933

EP - 5943

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 17

ER -

A strongly conservative finite element method for the coupling of Stokes and Darcy flow

Abstract

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