Some nonconforming mixed box schemes for elliptic problems

Numerical Methods for Partial Differential Equations

Volumn 18, Issue 3, 2002, Pages 355-373

  Croisille, Jean Pierre ^a   Greff, Isabelle ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Box scheme; Elliptic problems; Finite volume method; Hybridization; Petrov Galerkin mixed method

Indexed keywords

EID: 0036569995     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10003     Document Type: Article

References (25)

1. B. Courbet and J. P. Croisille, Finite volume box schemes on triangular meshes, Math Model Numer, 32(5) (1998), 631-649.
2. J-P. Croisille, Finite volume box schemes and mixed methods, Math Model Numer, 34(5) (2000), 1087-1106.
3. H. B. Keller, A new difference scheme for parabolic problems, Numerical solutions of partial differential equations, II, B. Hubbard editor, New York, Academic Press, 1971, pp. 327-350.
4. J. F. Maitre, About a "natural" mixed finite element method relation with classical methods and applications. Talk at the ENUMATH 99, July 99, Jyveskyla, Finland.
5. D. N. Arnold and F. Brezzi, Mixed and non-conforming finite elements methods: implementation, postprocessing and error estimates, Math Model Numer Anal, 19(1) (1985), 7-32.
6. 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(3) (1985), 493-496.
7. R. E. Bank and D. J. Rose, Some error estimates for the box method, SIAM J Numer Anal, 24(4) (1987), 777-787.
8. W. Hackbusch, On first and second order box schemes, Computing, 41 (1989), 277-296.
9. R. A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems, SIAM J Numer Anal, 19(2) (1982), 349-357.
10. J-M. Thomas and D. Trujillo, Mixed Finite Volume methods, Int J Numer Meth in Eng, 45 (1999), to appear.
11. I. Babuška, Error-bounds for finite elements method, Numer Math, 16 (1971), 322-333.
12. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems, arising from lagrangian multipliers, R.A.I.R.O. 8(R-2) (1974), 129-151.
13. C. Bernardi, C. Canuto, and Y. Maday, Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem, SIAM J Numer Anal, 25(6) (1988), 1237-1271.
14. M. Crouzeix and P. A. Raviart, Conforming and non conforming finite element methods for solving the stationary Stokes equations I, R.A.I.R.O., 7(R-3) (1973), 33-76.
15. P. A. Raviart and J. M. Thomas, Primal hybrid finite element methods for second order elliptic equations, Math of Comp, 31(138) (1977), 391-413.
16. R, Hiptmair, Nonconforming mixed discretization of second order elliptic problems, Technische Universität München, Mathematisches Institut, M9404, 1994.
17. J. Douglas, Jr., J. E. Santos, D. Sheen, and X. Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, MAN, 33(4) (1999), 747-770.
18. T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math for Comput, 64(211) (1995), 943-972.
19. B. Courbet, Schémas boîte en réseau triangulaire, Rapport technique 18/3446 EN, (1992), ONERA, unpublished.
20. M. Fortin and M. Soulie, A non-conforming piecewise quadratic finite element on triangles, Int J Num Meth Eng, 19 (1983), 505-520.
21. M. Farhloul and M. Fortin, A non-conforming mixed finite element for second order elliptic problems, Num Meth PDE, 1997.
22. P. A. Raviart and J. M. Thomas, A mixed finite element method for 2nd order elliptic problems, Lecture Notes in Math, 606, Springer-Verlag, 1977, 292-315.
23. V. Girault, Cours de DEA, Université Paris 6, unpublished.
24. D. Braess, Finite Elements, Cambridge Univ. Press, 1997.
25. 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.