Free access
Issue
ESAIM: M2AN
Volume 39, Number 1, January-February 2005
Page(s) 7 - 35
DOI http://dx.doi.org/10.1051/m2an:2005007
Published online 15 March 2005
  1. Y. Achdou, C. Bernardi and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy's equations. Numer. Math. 96 (2003) 17–42. [CrossRef] [MathSciNet]
  2. M. Amara, D. Capatina-Papaghiuc, E. Chacón-Vera and D. Trujillo, Vorticity–velocity–pressure formulation for Navier–Stokes equations. Comput. Vis. Sci. 6 (2004) 47–52. [CrossRef] [MathSciNet]
  3. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains. Math. Meth. Appl. Sci. 21 (1998) 823–864. [CrossRef] [MathSciNet]
  4. C. Bègue, C. Conca, F. Murat and O. Pironneau, Les équations de Stokes et de Navier–Stokes avec des conditions aux limites sur la pression. Nonlinear Partial Differ. Equ. Appl., Collège de France Seminar IX (1988) 179–264.
  5. C. Bernardi, C. Canuto and Y. Maday, Un problème variationnel abstrait. Application d'une méthode de collocation pour les équations de Stokes. C.R. Acad. Sci. Paris série I 303 (1986) 971–974.
  6. C. Bernardi, C. Canuto and Y. Maday, Generalized inf-sup condition for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal. 25 (1988) 1237–1271. [CrossRef] [MathSciNet]
  7. S. Bertoluzza and V. Perrier, The mortar method in the wavelet context. ESAIM: M2AN 35 (2001) 647–673. [CrossRef] [EDP Sciences]
  8. D. Braess and R. Verfürth, A posteriori error estimators for the Raviart–Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431–2444. [CrossRef] [MathSciNet]
  9. D.-G. Calugaru, Modélisation et simulation numérique du transport de radon dans un milieu poreux fissuré ou fracturé. Problème direct et problèmes inverses comme outils d'aide à la prédiction sismique, Thesis, Université de Franche-Comté, Besançon (2002).
  10. M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numér. 7 (1973) 33–76.
  11. M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43 (2002) 57–74. [CrossRef] [MathSciNet]
  12. M. Discacciati and A. Quarteroni, Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations, in Proc. of ENUMATH, F. Brezzi Ed., Springer-Verlag (to appear).
  13. M. Discacciati and A. Quarteroni, Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations. Comput. Vis. Sci. 6 (2004) 93–104. [MathSciNet]
  14. F. Dubois, Vorticity–velocity–pressure formulation for the Stokes problem. Math. Meth. Appl. Sci. 25 (2002) 1091–1119. [CrossRef]
  15. F. Dubois, M. Salaün and S. Salmon, First vorticity–velocity–pressure scheme for the Stokes problem, Internal Report 356, Institut Aérotechnique, Conservatoire National des Arts et Métiers, France (2002) (submitted).
  16. P.J. Frey and P.-L. George, Maillages, applications aux éléments finis. Hermès, Paris (1999).
  17. P.-L. George and F. Hecht, Nonisotropic grids. Handbook of Grid Generation, J.F. Thompson, B.K. Soni & N.P. Weatherhill Eds., CRC Press (1998).
  18. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations, Theory and Algorithms . Springer–Verlag (1986).
  19. F. Hecht, Construction d'une base de fonctions P1 non conforme à divergence nulle dans Formula . RAIRO Anal. Numér. 15 (1981) 119–150. [MathSciNet]
  20. F. Hecht and O. Pironneau, FreeFem++, see www.freefem.org.
  21. H. Kawarada, E. Baba and H. Suito, Effects of spilled oil on coastal ecosystems, in the Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering 2000, CD-ROM proceedings (2001).
  22. H. Kawarada, E. Baba and H. Suito, Effects of wave breaking action on flows in tidal-flats, in Computational Fluid Dynamics for the 21st Century, M. Hafez, K. Morinishi and J. Périaux Eds., Springer. Notes on Numerical Fluid Mechanics 78 (2001) 275–289.
  23. W.J. Layton, F. Schieweck and I. Yotov, Coupling fluid flow with porous media flow, Preprint of the University of Magdebourg, report N° 22-01 (2001).
  24. J.-C. Nedelec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet]
  25. R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal. 19 (1982) 349–357. [CrossRef] [MathSciNet]
  26. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, Mathematical Aspects of Finite Element Methods. Springer, Berlin. Lect. Notes Math. 606 (1977) 292–315. [CrossRef]
  27. S. Salmon, Développement numérique de la formulation tourbillon–vitesse–pression pour le problème de Stokes. Thesis, Université Pierre et Marie Curie, Paris (1999).
  28. R. Temam, Theory and Numerical Analysis of the Navier–Stokes Equations . North-Holland (1977).
  29. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques . Wiley & Teubner (1996).

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