Finite volume box schemes on triangular meshes

Mathematical Modelling and Numerical Analysis

Volumn 32, Issue 5, 1998, Pages 631-649

  Courbet, B ^a   Croisille, J P ^b  

^a ONERA   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Box method; Box scheme; Crouzeix Raviart element; Finite volume scheme; Finite clement method; Mixed method; Poisson problem; Raviart Thomas element

Indexed keywords

EID: 0032391431     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an/1998320506311     Document Type: Article

References (26)

1. R. E. BANK, D. J. ROSE, Some error estimates for the box method, SIAM J. Numer. Anal., 24, 4, 1987, 777-787.
2. J. BARANGER, J. F. MAÎTRE, F. OUDIN, Connection between finite volume and mixed finite element methods, Math. Model. and Numer. Anal. (M2AN), to appear.
3. D. BRAESS, Finite Elemente, Springer Lehrbuch, 1991.
4. S. C. BRENNER, L. R. SCOTT, The mathematical theory of finite element methods, Texts in Applied Mathematics 15, Springer.
5. F. BREZZI, M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer Series in Comp. Math., 15, Springer Verlag, New-York, 1991.
6. F. CASIER, H. DECONNINCK, C. HIRSCH, A class of central bidiagonal schemes with implicit boundary conditions for the solution of Euler's equations, AIAA-83-0126, 1983.
7. J. J. CHATTOT, S. MALET, A "box-scheme" for the Euler equations, Lecture Notes in Math., 1270, Springer-Verlag, 1986, 52-63.
8. B. COURBET, Schémas boîte en réseau triangulaire, ONERA, 1992, unpublished.
9. B. COURBET, Schémas à deux points pour la simulation numérique des écoulements, La Recherche Aérospatiale, n° 4, 1990, 21-46.
10. 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.
11. M. CROUZEIX, P. A. RAVIART, Conforming and non conforming finite element methods for solving the stationary Stokes equations I, R.A.I.R.O. 7, 1973, R-3, 33-76.
12. P. EMONOT, Méthodes de volumes-éléments-finis: Application aux équations de Navier-Stokes et résultats de convergence, Thèse de l'Université de Lyon 1, France, 1992.
13. G. FAIRWEATHER, R. D. SAYLOR, The reformulation and numerical solution of certain nonclassical initial-boundary value problems, SIAM J. Sci. Stat. Comput., 12, 1, 1991, 127-144.
14. M. FARHLOUL, M. FORTIN, A new mixed finite element for the Stokes and elasticity problems, SIAM J. Numer. Anal., 30, 4, 1993, 971-990.
15. W. HACKBUSCH, On first and second order box schemes, Computing, 41, 1989, 277-296.
16. C. JOHNSON, Adaptive finite element method for diffusion and convection problems, Comp. Meth. in Appl. Mech. Eng., 82, 1990, 301-322.
17. 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.
18. P. C. MEEK, J. NORBURY, Nonlinear moving boundary problems and a Keller box scheme, SIAM J. Numer. Anal., 21, 5, 1984, 883-893.
19. R. A. NICOLAIDES, The covolume approach to computing incompressible flows, Incompressible Comp. Fluid Dynamics, M. P. Gunzberger, R. A. Nicolaides Ed., 1993, Cambridge Univ. Press.
20. R. A. NICOLAIDES, Direct discretization of planar div-curl problems, SIAM J. Numer. Anal., 29, 1, 1992, 32-56.
21. R. A. NICOLAIDES, X. WU, Covolume solutions of three dimensional div-curl equations, ICASE Report 95-4.
22. B. J. NOYE, Some three-level finite difference methods for simulating advection in fluids, Computers and Fluids, 19, 1, 1991, 119-140.
23. P. A. RAVIART, J. M. THOMAS. A mixed finite element method for 2nd order elliptic problems, Lecture Notes in Math., 606, Springer-Verlag, 1977, 292-315.
24. S. F. WORNOM, Application of compact difference schemes to the conservative Euler equations for one-dimensional flow, NASA TM 8326.
25. S. F. WORNOM, A two-point difference scheme for computing steady-state solutions to the conservative one-dimensional Euler equations, Computers and Fluids, 12, 1, 1984, 11-30.
26. S. F. WORNOM, M. M. HAFEZ, Implicit conservative schemes for the Euler equations, AIAA J., 24, 2, 1986, 215-233.