Connection between finite volume and mixed finite element methods
Baranger, Jacques ; Maitre, Jean-François ; Oudin, Fabienne
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996), p. 445-465 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1996__30_4_445_0,
     author = {Baranger, Jacques and Maitre, Jean-Fran\c cois and Oudin, Fabienne},
     title = {Connection between finite volume and mixed finite element methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {30},
     year = {1996},
     pages = {445-465},
     mrnumber = {1399499},
     zbl = {0857.65116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1996__30_4_445_0}
}

Baranger, Jacques; Maitre, Jean-François; Oudin, Fabienne. Connection between finite volume and mixed finite element methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) pp. 445-465. http://gdmltest.u-ga.fr/item/M2AN_1996__30_4_445_0/

[1] J. Baranger, P. Emonot, J.-F. Maitre, 1992, High order lagrangian finite volume elements for elliptic boundary value problems, Numerical Methods in Engineering 92, Ch. Hirsch et al. ed., Elsevier Science Publishers, pp. 709-713.

[2] J. Baranger, J.-F Maitre, F. Oudin, 1994, Application de la théorie des éléments finis mixtes à l'étude d'une classe de schémas aux volumes différences finis pour les problèmes elliptiques, C.R. Acad. Sci. Paris, 319, Série I, pp.401-404. | MR 1289320 | Zbl 0804.65102

[3] F. Brezzi, M. Fortin, 1991, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, 15, Springer-Verlag, New-York. | MR 1115205 | Zbl 0788.73002

[4] P. G. Ciarlet, P.A. Raviart, 1972, General Lagrange and Hermite interpolation in Rn with applications to finite element methods, Arch. Rat. Mech. Anal., 46, pp. 177-199. | MR 336957 | Zbl 0243.41004

[5] I. Faille, 1992, A control volume method to solve an elliptic equation on a two-dimensional irregular mesh, Comput. Methods Appl. Mech. Engrg,, 100, pp. 275-290. | MR 1187634 | Zbl 0761.76068

[6] I. Faille, T. Gallouet, R. Herbin, 1991, Des mathématiciens découvrent les volumes finis, S.M.A.I., Matapli, Bulletin de liaison, 28.

[7] M. Farhloul, 1991, Méthodes d'éléments finis mixtes et volumes finis, Thèse, Université Laval, Québec.

[8] D. A. Jr. Forsyth, P. H. Sammon, 1988, Quadratic convergence for cell-centered grids, Applied Numerical Mathematics, 4, pp. 377-394. | MR 948505 | Zbl 0651.65086

[9] W. Hackbusch, 1989, On first and second order box schemes, Computing, 41, pp. 277-296. | MR 993825 | Zbl 0649.65052

[10] Y. Haugazeau, P. Lacoste, 1993, Condensation de la matrice de masse pour les éléments finis mixtes de H (rot), C.R. Acad. Sci. Paris, 316, Série I, pp. 509-512. | MR 1209276 | Zbl 0767.65076

[11] R. Herbin, An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, accepted for publication in Num. Meth. P.D.E. | MR 1316144 | Zbl 0822.65085

[12] K. W. Morton, E. Suli, 1991, Finite volume methods and their analysis, IMA Journal of Num. Anal., 11,pp. 241-260. | MR 1105229 | Zbl 0729.65087

[13] J. C. Nedelec, 1991, Notions sur les techniques d'éléments finis, Mathématiques et Applications, 7, Ellipses-Edition Marketing. | Zbl 0847.65078

[14] P. A. Raviart, J. M. Thomas, 1977, A mixed finite element method for second order elliptic problems, Mathematical Aspects of the Finite Element Methods (I. Galligani, E. Magenes, eds), Lectures Notes in Math., 606, Springer-Verlag, New-York. | MR 483555 | Zbl 0362.65089

[15] J. E. Roberts, J. M. Thomas, 1989, Mixed and hybrid methods, in Handbook of Numerical Analysis, (P. G. Ciarlet and J. L. Lions, eds.), Vol. II, Finite Element Methods (Part 1), North-Holland, Amsterdam. | MR 1115239 | Zbl 0875.65090

[16] A. Weiser,M. F. Weeler 1988, On convergence of block-centered finite differences for elliptic problems, SIAM J. Numer. Anal., 25, pp.351-375. | MR 933730 | Zbl 0644.65062