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More pressure in the finite element discretization of the Stokes problem

Published online by Cambridge University Press:  15 April 2002

Christine Bernardi
Analyse Numérique, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. (
Frédéric Hecht
Analyse Numérique, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. (
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For the Stokes problem in a two- or three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we derive some error estimates.

Research Article
© EDP Sciences, SMAI, 2000

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K. Arrow, L. Hurwicz and H. Uzawa, Studies in Nonlinear Programming. Stanford University Press, Stanford (1958).
Babuska, I., The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. CrossRef
C. Bergé, Théorie des graphes. Dunod, Paris (1970).
Boland, J. and Nicolaides, R., Stability of finite elements under divergence constraints. SIAM J. Numer. Anal. 20 (1983) 722-731. CrossRef
F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO - Anal. Numér. 8 R2 (1974) 129-151.
P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in the Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.-L. Lions Eds., North-Holland, Amsterdam (1991) 17-351.
P. Clément, Développement et applications de méthodes numériques volumes finis pour la description d'écoulements océaniques. Thesis, Université Joseph Fourier, Grenoble (1996).
M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO - Anal. Numér. 7 R3 (1973) 33-76.
P. Emonot, Méthodes de volumes éléments finis: application aux équations de Navier-Stokes et résultats de convergence. Thesis, Université Claude Bernard, Lyon (1992).
M. Fortin, An analysis of the convergence of mixed finite element methods. RAIRO - Anal. Numér. 11 R3 (1977) 341-354.
V. Girault and P.-A. Raviart, Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms. Springer-Verlag, Berlin (1986).
F. Hecht, Construction d'une base d'un élément fini P 1 non conforme à divergence nulle dans $\mathbb{R}^3$ . Thesis, Université Pierre et Marie Curie, Paris (1980).
Hecht, F., Construction d'une base de fonctions P 1 non conforme à divergence nulle dans $\mathbb{R}^3$ . RAIRO - Anal. Numér. 15 (1981) 119-150. CrossRef
Verfürth, R., Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO - Anal. Numér. 18 (1984) 175-182. CrossRef