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Numerische Mathematik

, Volume 53, Issue 1–2, pp 225–235 | Cite as

Stabilized mixed methods for the Stokes problem

  • Franco Brezzi
  • Jim DouglasJr.
Article

Summary

The solution of the Stokes problem is approximated by three stabilized mixed methods, one due to Hughes, Balestra, and Franca and the other two being variants of this procedure. In each case the bilinear form associated with the saddle-point problem of the standard mixed formulation is modified to become coercive over the finite element space. Error estimates are derived for each procedure.

Subject Classifications

AMS(MOS): 65N30 CR: G1.8 

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References

  1. 1.
    Brezzi, F., Pitkäranta, J.: On the stabilization of Finite Element Approximations of the Stokes Problem. In: Efficient Solutions of Elliptic Systems, Notes on Numerical Fluid Mechanics, Vol. 10 (W. Hackbusch, ed.), pp. 11–19. Braunschweig, Wiesbaden: Viewig 1984Google Scholar
  2. 2.
    Girault, V., Raviart, P.A.: Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Berlin Heidelberg New York: Springer 1986Google Scholar
  3. 3.
    Hughes, T.J.R., Franca, L.P., Balestra, M.: A New Finite Element Formulation for Computational Fluid Mechanics: V. Circumventing the Babuška-Brezzi condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal Order Interpolation. Comput. Methods Appl. Mech. Eng.59, 85–99 (1986)Google Scholar
  4. 4.
    Nitsche, J.A.: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Semin. Univ. Hamburg36, 9–15 (1970/1971)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Franco Brezzi
    • 1
    • 2
  • Jim DouglasJr.
    • 3
  1. 1.Dipartimento di Meccanica StrutturaleUniversità di PaviaPaviaItaly
  2. 2.Istituto di Analisi Numerica del C.N.R. di PaviaItaly
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

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