New nonconforming finite elements for solving the incompressible Navier-Stokes equations

  • P. Knobloch
Conference paper


We introduce a new class of nonconforming finite elements suitable for an accurate approximation of convection-dominated effects and of divergence-free functions and hence also well-suited for the numerical solution of the incompressible Navier-Stokes equations.


Space Versus Patch Test Finite Element Space Nodal Functional Nonconforming Element 
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  1. [1]
    Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New YorkMATHCrossRefGoogle Scholar
  2. [2]
    Ciarlet, P.G. (1991): Basic error estimates for elliptic problems. In: Ciarlet, P.G., Lions, J.-L. (eds.): Handbook of numerical analysis. vol. II. Finite element methods. Part I. North-Holland, Amsterdam, pp. 17–351Google Scholar
  3. [3]
    Crouzeix, M., Raviart, P.-A. (1973): Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. Rev. Française Automat. Informat. Recherche Opérationelle Sér, Rouge 7(R-3), 33–76MathSciNetGoogle Scholar
  4. [4]
    Girault, V., Raviart, P.-A. (1986): Finite element methods for Navier-Stokes equations. Theory and algorithms. Springer, BerlinMATHCrossRefGoogle Scholar
  5. [5]
    John, V., Maubach, J.M., Tobiska, L. (1997): Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Numer. Math. 78, 165–188MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Knobloch, P. (2000): On Korn’s inequality for nonconforming finite elements. Tech. Mech. 20, 205–214; Errata, ibid. 375Google Scholar
  7. [7]
    Knobloch, P. (2001): On the inf-sup condition for the P 1mod element. Preprint MATH-KNM-200l/4. Charles University, PragueGoogle Scholar
  8. [8]
    Knobloch, P., Tobiska, L. (1999): The P 1mod element: a new nonconforming finite element for convection-diffusion problems. Preprint 99–28. Fakultät für Mathematik, Otto-von-Guericke-Universität, MagdeburgGoogle Scholar
  9. [9]
    Temam, R. (1977): Navier-Stokes equations. Theory and numerical analysis. North-Holland, AmsterdamGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • P. Knobloch
    • 1
  1. 1.Institute of Numerical Mathematics Faculty of Mathematics and PhysicsCharles UniversityPrahaCzech Republic

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