Free Access
Volume 35, Number 1, January/February 2001
Page(s) 57 - 89
Published online 15 April 2002
  1. C. Amrouche and V. Girault, Decomposition of Vector spaces and application to the Stokes problem in arbitrary dimensions. Czeschoslovak Math. J. 44 (1994) 109-140. [Google Scholar]
  2. O. Besson and M. R. Laydi, Some estimates for the anisotropic Navier- Stokes equations and for the hydrostatic approximation. RAIRO-Modél. Math. Anal. Numér. 26 (1992) 855-865. [Google Scholar]
  3. I. Babuška, The Finite Element Method with Lagrange multipliers. Numer. Math. 20 (1973) 179-192. [CrossRef] [Google Scholar]
  4. C. Baiocchi, F. Brezzi and L. P. Franca, Virtual Bubbles and Galerkin-least-squares type methods (Ga.L.S.). Comput. Methods Appl. Mech. Engrg. 105 (1993) 125-141. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag, Berlin (1992). [Google Scholar]
  6. H. Brézis, Analyse Fonctionnelle. Masson, Paris (1983). [Google Scholar]
  7. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange Multipliers. RAIRO-Anal. Numér. R2 (1974) 129-151. [Google Scholar]
  8. F. Brezzi and J. Douglas, Stabilized mixed methods for the Stokes problem. Numer. Math. 53 (1988) 225-236. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Brezzi and J. Pitkäranta, On the stabilization of Finite Element approximations of the Stokes problem, in Efficient Solutions for Elliptic Systems. Notes on Numerical Fluid Mechanics 10, W. Hackbusch Ed., Springer-Verlag, Berlin (1984) 11-19. [Google Scholar]
  10. T. Chacón Rebollo, A term by term Stabilization Algorithm for Finite Element solution of incompressible flow problems. Numer. Math. 79 (1998) 283-319. [CrossRef] [MathSciNet] [Google Scholar]
  11. T. Chacón Rebollo and A. Domínguez Delgado, A unified analysis of Mixed and Stabilized Finite Element Solutions of Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 182 (2000) 301-331. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Chacón Rebollo and F. Guillén González, An intrinsic analysis of existence of solutions for the hydrostatic approximation of Navier-Stokes equations. C. R. Acad. Sci. Paris, Série I 330 (2000) 841-846. [Google Scholar]
  13. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). [Google Scholar]
  14. L.P. Franca and S.L. Frey, Stabilized Finite Elements: II. The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233. [CrossRef] [MathSciNet] [Google Scholar]
  15. L.P. Franca and R. Stenberg, Error analysis fo some Galerkin-Least-Squares methods for the elasticity equations. SIAM J. Numer. Anal. 28 (1991) 1680-1697. [Google Scholar]
  16. L.P. Franca, T.J.R. Hughes and R. Stenberg, Stabilized Finite Element Methods, in Incompressible Computational Fluid Dynamics, M.D. Gunzburger and R.A. Nicolaides Eds., Cambridge Univ. Press, New York (1993). [Google Scholar]
  17. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes equations. Springer-Verlag, Berlin (1988). [Google Scholar]
  18. R. Dautray and L.L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques. Masson, Paris (2000). [Google Scholar]
  19. P. Gervasio and F. Saleri, Stabilized Spectral Element approximation for the Navier-Stokes equations. Numer. Methods Partial Differential Eq. 14 (1988) 115-141. [Google Scholar]
  20. T.J.R. Hughes and L.P. Franca, A new Finite Element formulation for CFD: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces. Comput. Methods Appl. Mech. Engrg. 65 (1987) 85-96. [CrossRef] [MathSciNet] [Google Scholar]
  21. T.J.R. Hughes, L.P. Franca and M. Balestra, A new Finite Element formulation for CFD: V. Circumventing the Brezzi-Babuška condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl Mech. Engrg. 59 (1986) 85-99. [Google Scholar]
  22. P. Knobloch and L. Tobiska, Stabilization methods of Bubble type for the Q1-Q1-Element applied to the incompressible Navier-Stokes equations. ESAIM: M2AN 34 (2000) 85-107. [CrossRef] [EDP Sciences] [Google Scholar]
  23. R. Lewandowski, Analyse Mathématique et Océanographie. Masson, Paris (1997). [Google Scholar]
  24. J.L. Lions, R. Temam and S. Wang, New formulation of the primitive equations of the atmosphere and applications. Nonlinearity 5 (1992) 237-288. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Pierre, Simple C0-approximations for the computation of incompressible flows. Comput. Methods Appl Mech. Engrg. 68 (1989) 205-228. [Google Scholar]
  26. G. Russo, Bubble stabilization of Finite Element Methods fo the linearized incompressible Navier-Stokes equations. Comput. Methods Appl Mech. Engrg. 132 (1996) 335-343. [Google Scholar]
  27. L. Tobishka and R. Verfürth, Analysis of a Streamline Diffusion finite element method for the Stokes and Navier-Stokes equations. SIAM J. Numer. Anal. 33 (1996) 107-127. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Verfürth, Analysis of some Finite Element solutions for the Stokes Problem. RAIRO-Anal. Numér. 18 (1984) 175-182. [Google Scholar]

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