• Ulrich Wilbrandt
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)


Flows in domains which are partly occupied by a porous medium are of great interest and importance, noticeable examples include groundwater—surface water flow, as well as air and oil filters, blood filtration through vessel walls, and fuel cells.


  1. [Ang11]
    Philippe Angot. On the well-posed coupling between free fluid and porous viscous flows. Appl. Math. Lett., 24(6):803–810, 2011.MathSciNetCrossRefGoogle Scholar
  2. [CGH+10]
    Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, and Weidong Zhao. Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. SIAM J. Numer. Anal., 47(6):4239–4256, 2010.MathSciNetCrossRefGoogle Scholar
  3. [CGHW10]
    Yanzhao Cao, Max Gunzburger, Fei Hua, and Xiaoming Wang. Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. Commun. Math. Sci., 8(1):1–25, 2010.MathSciNetCrossRefGoogle Scholar
  4. [CGHW11]
    Wenbin Chen, Max Gunzburger, Fei Hua, and Xiaoming Wang. A parallel robin-robin domain decomposition method for the Stokes-Darcy system. SIAM J. Numerical Analysis, 49(3):1064–1084, 2011.MathSciNetCrossRefGoogle Scholar
  5. [DQ09]
    M. Discacciati and A. Quarteroni. Navier-Stokes/Darcy coupling: modeling, analysis and numerical approximation. Revista Matematica Complutense, 22(2):315–426, 2009.MathSciNetzbMATHGoogle Scholar
  6. [DQV07]
    Marco Discacciati, Alfio Quarteroni, and Alberto Valli. Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. SIAM J. Numer. Anal., 45(3):1246–1268, 2007.MathSciNetCrossRefGoogle Scholar
  7. [GOS11a]
    Gabriel N. Gatica, Ricardo Oyarzúa, and Francisco-Javier Sayas. Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem. Math. Comp., 80(276):1911–1948, 2011.MathSciNetCrossRefGoogle Scholar
  8. [JM00]
    Willi Jäger and Andro Mikelić. On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math., 60(4):1111–1127, 2000.MathSciNetCrossRefGoogle Scholar
  9. [LSY02]
    William J. Layton, Friedhelm Schieweck, and Ivan Yotov. Coupling fluid flow with porous media flow. SIAM J. Numer. Anal., 40(6):2195–2218 (2003), 2002.MathSciNetCrossRefGoogle Scholar
  10. [RY05]
    Béatrice Rivière and Ivan Yotov. Locally conservative coupling of Stokes and Darcy flows. SIAM J. Numer. Anal., 42(5):1959–1977, 2005.MathSciNetCrossRefGoogle Scholar
  11. [Saf71]
    P.G. Saffman. On the boundary condition at the interface of a porous medium. Stud. Appl. Math., 50:93–101, 1971.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ulrich Wilbrandt
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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