Abstract
The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.
Similar content being viewed by others
References
V. Girault, P. A. Raviart: Finite Element Approximation of the Navier-Stokes Equations. Springer-Verlag, Berlin, 1979.
I. Hlaváček, M. Křížek: Internal finite element approximations in the dual variational methods for second order elliptic problems with curved boundaries. Apl. Mat. 29 (1984), 52–69.
M. Křížek, P. Neittaanmäki: Internal FE approximation of spaces of divergence-free functions in 3-dimensional domains. Internat. J. Numer. Methods Fluids 6 (1986), 811–817.
M. Křížek, P. Neittaanmäki: Finite Element Approximation of Variational Problems and Applications. Longman Scientific & Technical, Harlow, 1990.
J. C. Nedelec: Eléments finis mixtes incompressibles pour l'equation de Stokes dans ℝ3. Numer. Math. 39 (1982), 97–112.
R. Temam: Navier-Stokes Equations. North-Holland, Amsterdam, 1979.
V. S. Vladimirov: Equations of Mathematical Physics. Marcel Dekker, New York, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Korotov, S. On equilibrium finite elements in three-dimensional case. Applications of Mathematics 42, 233–242 (1997). https://doi.org/10.1023/A:1022421722236
Issue Date:
DOI: https://doi.org/10.1023/A:1022421722236