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Subproblems Individually

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

Abstract

In this section the existence and uniqueness of solutions of the involved subproblems are proved. Besides the Laplace equation this includes the so-called saddle point theory which is an abstract framework and is then applied to the Stokes equations as well as to the coupled Stokes–Darcy problem in Chap.  6.

References

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    Daniele Boffi, Franco Brezzi, and Michel Fortin. Mixed finite element methods and applications, volume 44 of Springer Series in Computational Mathematics. Springer, Heidelberg, 2013.CrossRefGoogle Scholar
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    Franco Brezzi and Michel Fortin. Mixed and hybrid finite element methods, volume 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York, 1991.CrossRefGoogle Scholar
  3. [GR86]
    Vivette Girault and Pierre-Arnaud Raviart. Finite element methods for Navier-Stokes equations, volume 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1986. Theory and algorithms.Google Scholar
  4. [QV99]
    Alfio Quarteroni and Alberto Valli. Domain decomposition methods for partial differential equations. Numerical Mathematics and Scientific Computation. The Clarendon Press Oxford University Press, New York, 1999. Oxford Science Publications.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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