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Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition

Numerische Mathematik volume 117, pages 601–629 (2011)Cite this article

Abstract

Domain decomposition methods for solving the coupled Stokes–Darcy system with the Beavers–Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36830, USA

    Yanzhao Cao

  2. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306-4120, USA

    Max Gunzburger & Xiaoming He

  3. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Xiaoming He

  4. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    Xiaoming Wang

Authors
  1. Yanzhao Cao
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  2. Max Gunzburger
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  3. Xiaoming He
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  4. Xiaoming Wang
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Corresponding author

Correspondence to Xiaoming He.

Additional information

This work is supported in part by the CMG program of the National Science Foundation under grant numbers DMS-0620035 (for MG, XH, and XW) and DMS-0914554 (for YC).

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Cao, Y., Gunzburger, M., He, X. et al. Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition. Numer. Math. 117, 601–629 (2011). https://doi.org/10.1007/s00211-011-0361-8

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  • DOI: https://doi.org/10.1007/s00211-011-0361-8

Mathematics Subject Classification (2010)

  • 65M55
  • 65M12
  • 65M15
  • 65M60
  • 35M10
  • 35Q35
  • 76D07
  • 76S05