Skip to main content
SpringerLink
Log in

Incompressible mixed finite elements for the Stokes' equation in IR3

  • Contributed Papers
  • Conference paper
  • First Online:
Seventh International Conference on Numerical Methods in Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 141))

  • 161 Accesses

Abstract

In this paper, we study a new family of mixed finite elements for the Stokes' equation. These elements are exactly incompressible, but they are not conforming for the velocity. When studying the Navier-Stokes' equation, this nonconformity permits us to introduce an upwind scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. CIARLET, P.G., RAVIART, P.A., A mixed finite element method for the biharmonic equation, in “Mathematical Aspects in Finite Element Equation”, C. de Boor (ed.), Academic Press, New York, 1974, 125–145.

    Google Scholar 

  2. FORTIN, M., Résolution numérique des équations de Navier-Stokes par des étéments finis de type mixte, 2nd International Symposium on Finite Element Methods in Flow Problems, S. Margherita Ligure, Italy, 1976.

    Google Scholar 

  3. GIRAULT, V., RAVIART, P.A., Finite etement approximation of the Navier-Stokes equations, Lecture Notes on Mathematics n° 749, Springer Verlag, Berlin-Heidelberg-New York, 1979.

    Google Scholar 

  4. GLOWINSKI, R., Approximations externes par éléments finis d'ondre un et deux du problèm de Dirichlet pour Δ2; “Topics in Numerical Analysis I”, J.J.H. Miller (ed.), Academic Press, London, 1973, 123–171.

    Google Scholar 

  5. LIONS, J.L., Quelques méthodes de résoluti.on des pnoblèmes aux limites non linéaires, Dunod, Paris, 1969.

    Google Scholar 

  6. NEDELEC, J.C., Mixed finite ekements in IR3 Rapport Interne n° 49, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1979.

    Google Scholar 

  7. RAVIART, P.A., Méthodes d'éléments finis pour les équations de Navier-Stokes, Cours de l'Ecole d'été EDF-CEA-IRIA, 1979.

    Google Scholar 

  8. TEMAM, R., Navier-Stokes equations, North Holland, Amsterdam, 1977.

    Google Scholar 

  9. SCHOLZ, R., A mixed method for 4th order problems using linear finite etements, RAIRO, Analyse Numérique, 12 (1978), 85–90.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Mathématiques Appliquées (ERA/CNRS 343) — Ecole Polytechnique, 91128, Palatseau Cedex, France

    J. C. Nedelec

Authors
  1. J. C. Nedelec
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

W. C. Reynolds R. W. MacCormack

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Nedelec, J.C. (1981). Incompressible mixed finite elements for the Stokes' equation in IR3 . In: Reynolds, W.C., MacCormack, R.W. (eds) Seventh International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10694-4_45

Download citation

  • DOI: https://doi.org/10.1007/3-540-10694-4_45

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10694-4

  • Online ISBN: 978-3-540-38624-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation