no. 5
Finite volume box schemes on triangular meshes
ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 5, pp. 631-649 
@article{M2AN_1998__32_5_631_0,
     author = {Courbet, B. and Croisille, J. P.},
     title = {Finite volume box schemes on triangular meshes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {631--649},
     year = {1998},
     publisher = {Elsevier},
     volume = {32},
     number = {5},
     mrnumber = {1643473},
     zbl = {0920.65065},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1998__32_5_631_0/}
}
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Courbet, B.; Croisille, J. P. Finite volume box schemes on triangular meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 5, pp. 631-649. https://www.numdam.org/item/M2AN_1998__32_5_631_0/

[1] R. E. Bank, D. J. Rose, Some error estimates for the box method, SIAM J. Numer. Anal, 24, 4, 1987, 777-787. | Zbl | MR

[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. | Zbl | MR | Numdam

[3] D. Braess, Finite Elemente, Springer Lehrbuch, 1991. | Zbl

[4] S. C. Brenner, L. R. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics 15, Springer. | Zbl

[5] F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Comp. Math., 15, Springer Verlag, New-York, 1991. | Zbl | MR

[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. | Zbl | MR

[8] B. Courbet, Schémas boîte en réseau triangulaire, ONERA, 1992, unpublished.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. | Zbl

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

[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. | Zbl | MR

[15] W. Hackbusch, On first and second order box schemes, Computing, 41, 1989, 277-296. | Zbl | MR

[16] C. Johnson, Adaptive finite element method for diffusion and convection problems, Comp. Meth. in Appl. Mech. Eng., 82, 1990, 301-322. | Zbl | MR

[17] H. B. Keller, A new difference scheme for parabolic problems, Numerical solutions of partial differential equations, II, B. Hubbard éd., Academic Press, New-York, 1971, 327-350. | Zbl | MR

[18] P. C. Meek, J. Norbury, Nonlinear moving boundary problems and a Keller box scheme, SIAM J. Numer. Anal., 21, 5, 1984, 883-893. | Zbl | MR

[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. | Zbl | MR

[21] R. A. Nicolaides, X. Wu, Covolume solutions of three dimensional div-curl equations, ICASE Report 95-4. | Zbl

[22] B. J. Noye, Some three-level finite difference methods for simulating advection in fluids, Computers and Fluids, 19, 1991, 119-140. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl

[26] S. F. Wornom, M. M. Hafez, Implicit conservative schemes for the Euler equations, AIAA J., 24, 2, 1986, 215-233. | Zbl | MR