Skip to main content
SpringerLink
Log in

Finite element solution of 3D viscous flow problems using nonstandard degrees of freedom

  • Published:
Japan Journal of Applied Mathematics Aims and scope Submit manuscript

Abstract

Two velocity-pressure finite element methods for solving incompressible flow problems in three-dimension space are studied. The velocity is defined by means of a new type of degree of freedom called parametrized. Though nonconforming in velocity, optimal convergence results are proven to hold for both methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. A. Adams, Sobolev Spaces. Academic Press, New York, 1975.

    MATH  Google Scholar 

  2. F. Brezzi, On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO Anal. Numér.,8-R2 (1974), 120–151.

    Google Scholar 

  3. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978.

    MATH  Google Scholar 

  4. M. Crouzeix and P. A. Raviart, Conforming and nonconforming finite element methods for solving stationary Stokes’ equations (I). RAIRO,R-3 (1973) 33–76.

    MathSciNet  Google Scholar 

  5. M. Fortin, Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthode des éléments finis. Thèse de Doctorat d’Etat, Univ. Pierre et Marie Curie, Paris, 1972.

    Google Scholar 

  6. V. Girault and P. A. Raviart Finite Element Approximation of the Navier-Stokes Equations. Lecture Notes in Math., Springer-Verlag, Berlin, 1979.

    Book  MATH  Google Scholar 

  7. P. A. Raviart and J. M. Thomas, Introduction à l’Analyse Numérique des Équations aux Derivées Partielles, Masson, Paris, 1983.

    MATH  Google Scholar 

  8. V. Ruas, Méthodes d’éléments finis en élasticité incompressible non linéaire et diverses contributions à l’approximation des problèmes aux limites. Thèse de Doctorat d’Etat. Univ. Pierre et Marie Curie, Paris, 1982.

    Google Scholar 

  9. V. Ruas, Une méthode d’éléments finis non conformes en vitesse pour le probléme de Stokes tridimensionnel. Mat. Apl. e Comp.,1 (1982), 53–73.

    MATH  MathSciNet  Google Scholar 

  10. V. Ruas, A complete three-dimensional version of the quadratic velocity-constant pressure finite element method for fluid flow problems. Rev. Brasil. Comps,3, No. 2 (1983/1984), 91–97.

    Google Scholar 

  11. R. Stenberg, Analysis of mixed finite element methods for the Stokes problem: a unified approach. Math. Comp.,42 (1984), 9–32.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departmento de Informática, Pontifícia Universidade Católica, 22.453, Rio de Janeiro, Brazil

    Vitoriano Ruas Santos

Authors
  1. Vitoriano Ruas Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Santos, V.R. Finite element solution of 3D viscous flow problems using nonstandard degrees of freedom. Japan J. Appl. Math. 2, 415–431 (1985). https://doi.org/10.1007/BF03167084

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167084

Key words

Search

Navigation