Finite Volume Box Schemes and Mixed Methods
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 34, Issue: 5, page 1087-1106
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- 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.
- 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.
- I. Babuska, Error-Bounds for Finite Elements Method. Numer. Math.16 (1971) 322-333.
- R.E. Bank and D.J. Rose, Some error estimates for the box method. SIAM J. Numer. Anal.24 (1987) 777-787.
- 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.
- 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 I19 (1986) 971-974.
- 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.
- D. Braess, Finite Elements. Cambridge Univ. Press (1997).
- S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Texts Appl. Math.15 (1994) Springer, New-York.
- F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems, arising from lagrangian multipliers. RAIRO8 (1974) R-2, 129-151.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Series Comp. Math.15, Springer Verlag, New-York (1991).
- 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.
- 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.
- 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).
- J.J. Chattot, Box-schemes for First Order Partial Differential Equations. Adv. Comp. Fluid Dynamics, Gordon Breach Publ. (1995) 307-331.
- J.J. Chattot, A Conservative Box-scheme for the Euler Equations. Int. J. Num. Meth. Fluids (to appear).
- J.J. Chattot and S. Malet, A box-schemefor the Euler equations. Lect. Notes Math.1270, Springer-Verlag, Berlin (1987) 82-99.
- 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.
- B. Courbet, Schémas boîte en réseau triangulaire, Rapport technique 18/3446 EN (1992), ONERA, unpublished.
- B. Courbet, Schémas à deux points pour la simulation numérique des écoulements, La Recherche Aérospatiale n°4 (1990) 21-46.
- 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.
- B. Courbet and J.P. Croisille, Finite Volume Box Schemes on triangular meshes. Math. Model. Numer.32 (1998) 631-649.
- J-P. Croisille, Finite Volume Box Schemes, in Proc. of the 2nd Int. Symp. on Finite Volume for Complex Applications. Hermes, Paris (1999).
- M. Crouzeix and P.A. Raviart, Conforming and non conforming finite element methods for solving the stationary Stokes equations I. RAIRO7 (1973) R-3, 33-76.
- F. Dubois, Finite volumes and mixed Petrov-Galerkin finite elements; the unidimensional problem. Num. Meth. PDE (to appear).
- R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, in Handbook of Numerical Analysis, Ciarlet-Lions Eds. 5 (1997).
- 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.
- L. Fezoui and B. Stoufflet, A class of implicit upwind schemes for Euler equations on unstructured grids. J. Comp. Phys.84 (1989) 174-206.
- V. Girault and P.A. Raviart, Finite Element Approximation of the Navier-Stokes equations. Lect. Notes Math.749, Springer, Berlin (1979).
- W. Hackbusch, On first and second order box schemes. Computing41 (1989) 277-296.
- 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.
- 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).
- 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.
- P.C. Meek and J. Norbury, Nonlinear moving boundary problems and a Keller box scheme. SIAM J. Numer. Anal.21 (1984) 883-893.
- R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal.19 (1982) 349-357.
- 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.
- E. Süli, Convergence of finite volume schemes for Poisson's equation on non-uniform meshes. SIAM J. Numer. Anal.28 (1991) 1419-1430.
- E. Süli, The accuracy of cell vertex finite volume methods on quadrilateral meshes. Math. of Comp.59 (1992) 359-382.
- T. Schmidt, Box Schemes on quadrilateral meshes. Computing51 (1993) 271-292.
- J-M Thomas and D. Trujillo, Mixed Finite Volume methods. Int. J. Num. Meth. Eng.45 (1999) to appear.
- S.F. Wornom, Application of compact difference schemes to the conservative Euler equations for one-dimensional flows. NASA Tech. Mem.83262 (1982).
- S.F. Wornom and M.M. Hafez, Implicit conservative schemes for the Euler equations. AIAA J.24 (1986) 215-233.
- 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.
Citations in EuDML Documents
top- Alexandre Ern, Jean-Luc Guermond, Evaluation of the condition number in linear systems arising in finite element approximations
- Linda El Alaoui, Alexandre Ern, Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
- Linda El Alaoui, Alexandre Ern, Residual and hierarchical error estimates for nonconforming mixed finite element methods
- Kwang Y. Kim, New mixed finite volume methods for second order eliptic problems