Uniform inf-sup conditions for the spectral discretization of the stokes problem

Mathematical Models and Methods in Applied Sciences

Volumn 9, Issue 3, 1999, Pages 395-414

  Bernardi, C ^a   Maday, Y ^a,b  

^a CNRS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033472482     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202599000208     Document Type: Article

References (22)

1. M. Azaïez, Méthodes spectrales et des éléments spectraux pour la mécanique des fluides, Habilitation à Diriger des Recherches, Université Paul Sabatier, Toulouse (1997).
2. I. Babuška, The finite element method with Lagrangian multipliers, Numer. Math. 20 (1973) 179-192.
3. C. Bernardi, M. Dauge and Y. Maday, Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube, in Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, eds. M. Costabel, M. Dauge and S. Nicaise, Lecture Notes in Pure and Applied Mathematics, Vol. 167 (Dekker, 1994) 27-46.
4. C. Bernardi, P. Fisher, Y. Maday and A. T. Patera, Spectral element methods, in The Handbook of Numerical Analysis, in preparation.
5. C. Bernardi and Y. Maday, Spectral methods, in The Handbook of Numerical Analysis V, eds. P. G. Ciarlet and J.-L. Lions (North-Holland, 1997).
6. C. Bernardi, Y. Maday and B. Métivet, Calcul de la pression dans la résolution spectrale du problème de Stokes, La Recherche Aérospatiale 1 (1987) 1-21.
7. J. Boland and R. Nicolaides, Stability of finite elements under divergence constraints, SIAM J. Numer. Anal. 20 (1983) 722-731.
8. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, R.A.I.R.O. Anal. Numér. 8 (1974) 129-151.
9. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer-Verlag, 1991).
10. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, 1987).
11. P. F. Fisher and E. M. Rønquist, Spectral element methods for large scale parallel Navier-Stokes calculations, Comput. Meth. Appl. Mech. Engrg. 116 (1994) 69-76.
12. M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O. Anal. Numér. 11 (1977) 341-354.
13. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms (Springer-Verlag, 1986).
14. Y. Maday, D. Meiron, A. T. Patera and E. M. Ronquist, Analysis of iterative methods for the steady and unsteady Stokes problem: application to spectral element discretizations, SIAM J. Sci. Comput. 14 (1993) 310-337.
15. Y. Maday, A. T. Patera and E. M. Rønquist, A well-posed optimal Legendre spectral element approximation of the Stokes semi-periodic problem, ICASE Report 87-48 (1987).
16. N-2 method for the approximation of the Stokes problem, Internal Report 92025, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris (1992), to appear in Numer. Math.
17. R. J. Nessel and G. Wilmes, On Nikolskii-type inequalities for orthogonal expansions, in Approximation Theory II, eds. G. G. Lorentz, C. K. Chui and L. L. Schumaker (Academic Press, 1976) 479-484.
18. E. M. Rønquist, A domain decomposition solver for the steady Navier-Stokes equations, Proc. Third Int. Conf. on Spectral and High Order Methods, Houston J. Math. (1995) 469-485.
19. G. Sacchi-Landriani and H. Vandeven, Polynomial approximation of divergence-free functions, Math. Comput. 52 (1989) 103-130.
20. R. Stenberg and M. Suri, Mixed hp finite element methods for problems in elasticity and Stokes flow, Numer. Math. 72 (1996) 367-389.
21. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis (North-Holland, 1977).
22. R. Verfürth, Error estimates for a mixed finite element approximation of the Stokes equations, R.A.I.R.O. Anal. Numér. 18 (1984) 175-182.