Free Access
Volume 34, Number 5, September/October 2000
Page(s) 1087 - 1106
Published online 15 April 2002
  1. B. Achchab, A. Agouzal, J. Baranger and J-F. Maître, Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes. Numer. Math. 80 (1998) 159-179. [CrossRef] [MathSciNet] [Google Scholar]
  2. D.N. Arnold and F. Brezzi, Mixed and non-conforming finite elements methods: implementation, postprocessing and error estimates. RAIRO - Modél. Math. Anal. Numér. 19 (1985) 7-32. [Google Scholar]
  3. I. Babuska, Error-Bounds for Finite Elements Method. Numer. Math. 16 (1971) 322-333. [CrossRef] [MathSciNet] [Google Scholar]
  4. R.E. Bank and D.J. Rose, Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777-787. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Baranger, J.F. Maître and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO - Modél. Math. Anal. Numér. 30 (1996) 445-465. [Google Scholar]
  6. C. Bernardi, C. Canuto and Y. Maday, Un problème variationnel abstrait. Application à une méthode de collocation pour les équations de Stokes. C. R. Acad. Sci. Paris, t.303, Série I 19 (1986) 971-974. [Google Scholar]
  7. C. Bernardi, C. Canuto and Y. Maday, Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal. 25 (1988) 1237-1271. [CrossRef] [MathSciNet] [Google Scholar]
  8. D. Braess, Finite Elements. Cambridge Univ. Press (1997). [Google Scholar]
  9. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Texts Appl. Math. 15 (1994) Springer, New-York. [Google Scholar]
  10. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems, arising from lagrangian multipliers. RAIRO 8 (1974) R-2, 129-151. [Google Scholar]
  11. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Series Comp. Math. 15, Springer Verlag, New-York (1991). [Google Scholar]
  12. F. Brezzi, J. Douglas and L.D. Marini, Two families of Mixed Finite Element for second order elliptic problems. Numer. Math. 47 (1985) 217-235. [CrossRef] [MathSciNet] [Google Scholar]
  13. Z. Cai, J. Mandel and S. McCormick, The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28 (1991) 392-402. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Casier, H. Deconninck and C. Hirsch, A class of central bidiagonal schemes with implicit boundary conditions for the solution of Euler's equations. AIAA-83-0126 (1983). [Google Scholar]
  15. J.J. Chattot, Box-schemes for First Order Partial Differential Equations. Adv. Comp. Fluid Dynamics, Gordon Breach Publ. (1995) 307-331. [Google Scholar]
  16. J.J. Chattot, A Conservative Box-scheme for the Euler Equations. Int. J. Num. Meth. Fluids (to appear). [Google Scholar]
  17. J.J. Chattot and S. Malet, A box-schemefor the Euler equations. Lect. Notes Math. 1270, Springer-Verlag, Berlin (1987) 82-99. [Google Scholar]
  18. Y. Coudière, J-P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. Math. Model. Numer. 33 (1999) 493-516. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. B. Courbet, Schémas boîte en réseau triangulaire, Rapport technique 18/3446 EN (1992), ONERA, unpublished. [Google Scholar]
  20. B. Courbet, Schémas à deux points pour la simulation numérique des écoulements, La Recherche Aérospatiale n°4 (1990) 21-46. [Google Scholar]
  21. B. Courbet, Étude d'une famille de schémas boîtes à deux points et application à la dynamique des gaz monodimensionnelle, La Recherche Aérospatiale n°5 (1991) 31-44. [Google Scholar]
  22. B. Courbet and J.P. Croisille, Finite Volume Box Schemes on triangular meshes. Math. Model. Numer. 32 (1998) 631-649. [Google Scholar]
  23. J-P. Croisille, Finite Volume Box Schemes, in Proc. of the 2nd Int. Symp. on Finite Volume for Complex Applications. Hermes, Paris (1999). [Google Scholar]
  24. M. Crouzeix and P.A. Raviart, Conforming and non conforming finite element methods for solving the stationary Stokes equations I. RAIRO 7 (1973) R-3, 33-76. [Google Scholar]
  25. F. Dubois, Finite volumes and mixed Petrov-Galerkin finite elements; the unidimensional problem. Num. Meth. PDE (to appear). [Google Scholar]
  26. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, in Handbook of Numerical Analysis, Ciarlet-Lions Eds. 5 (1997). [Google Scholar]
  27. G. Fairweather and R.D. Saylor, The reformulation and numerical solution of certain nonclassical initial-boundary value problems. SIAM J. Sci. Stat. Comput. 12 (1991) 127-144. [CrossRef] [Google Scholar]
  28. L. Fezoui and B. Stoufflet, A class of implicit upwind schemes for Euler equations on unstructured grids. J. Comp. Phys. 84 (1989) 174-206. [CrossRef] [Google Scholar]
  29. V. Girault and P.A. Raviart, Finite Element Approximation of the Navier-Stokes equations. Lect. Notes Math. 749, Springer, Berlin (1979). [Google Scholar]
  30. W. Hackbusch, On first and second order box schemes. Computing 41 (1989) 277-296. [CrossRef] [MathSciNet] [Google Scholar]
  31. H.B. Keller, A new difference scheme for parabolic problems, Numerical solutions of partial differential equations, II, B. Hubbard Ed., Academic Press, New-York (1971) 327-350. [Google Scholar]
  32. R.D. Lazarov, J.E. Pasciak and P.S. Vassilevski, Coupling mixed and finite volume discretizations of convection-diffusion-reaction equations on non-matching grids, in Proc. of the 2nd Int. Symp. on Finite Volume for Complex Applications, Hermes, Paris (1999). [Google Scholar]
  33. L.D. Marini, An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method. SIAM J. Numer. Anal. 22 (1985) 493-496. [CrossRef] [MathSciNet] [Google Scholar]
  34. P.C. Meek and J. Norbury, Nonlinear moving boundary problems and a Keller box scheme. SIAM J. Numer. Anal. 21 (1984) 883-893. [CrossRef] [MathSciNet] [Google Scholar]
  35. R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal. 19 (1982) 349-357. [CrossRef] [MathSciNet] [Google Scholar]
  36. P.A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems. Lect. Notes Math. 606, Springer-Verlag, Berlin (1977) 292-315. [Google Scholar]
  37. E. Süli, Convergence of finite volume schemes for Poisson's equation on non-uniform meshes. SIAM J. Numer. Anal. 28 (1991) 1419-1430. [CrossRef] [MathSciNet] [Google Scholar]
  38. E. Süli, The accuracy of cell vertex finite volume methods on quadrilateral meshes. Math. of Comp. 59 (1992) 359-382. [CrossRef] [MathSciNet] [Google Scholar]
  39. T. Schmidt, Box Schemes on quadrilateral meshes. Computing 51 (1993) 271-292. [CrossRef] [MathSciNet] [Google Scholar]
  40. J-M Thomas and D. Trujillo, Mixed Finite Volume methods. Int. J. Num. Meth. Eng. 45 (1999) to appear. [Google Scholar]
  41. S.F. Wornom, Application of compact difference schemes to the conservative Euler equations for one-dimensional flows. NASA Tech. Mem. 83262 (1982). [Google Scholar]
  42. S.F. Wornom and M.M. Hafez, Implicit conservative schemes for the Euler equations. AIAA J. 24 (1986) 215-233. [CrossRef] [MathSciNet] [Google Scholar]
  43. A. Younes, R. Mose, P. Ackerer and G. Chavent, A new formulation of the Mixed Finite Element Method for solving elliptic and parabolic PDE. J. Comp. Phys. 149 (1999) 148-167. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you