Connection between finite volume and mixed finite element methods

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1. [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. [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. Zbl0804.65102MR1289320
3. [3] F. BREZZI, M. FORTIN, 1991, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, 15, Springer-Verlag, New-York. Zbl0788.73002MR1115205
4. [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. Zbl0243.41004MR336957
5. [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. Zbl0761.76068MR1187634
6. [6] I. FAILLE, T. GALLOUET, R. HERBIN, 1991, Des mathématiciens découvrent les volumes finis, S.M.A.I., Matapli, Bulletin de liaison, 28. 
7. [7] M. FARHLOUL, 1991, Méthodes d'éléments finis mixtes et volumes finis, Thèse, Université Laval, Québec. 
8. [8] D. A. Jr. FORSYTH, P. H. SAMMON, 1988, Quadratic convergence for cell-centered grids, Applied Numerical Mathematics, 4, pp. 377-394. Zbl0651.65086MR948505
9. [9] W. HACKBUSCH, 1989, On first and second order box schemes, Computing, 41, pp. 277-296. Zbl0649.65052MR993825
10. [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. Zbl0767.65076MR1209276
11. [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. Zbl0822.65085MR1316144
12. [12] K. W. MORTON, E. SULI, 1991, Finite volume methods and their analysis, IMA Journal of Num. Anal., 11,pp. 241-260. Zbl0729.65087MR1105229
13. [13] J. C. NEDELEC, 1991, Notions sur les techniques d'éléments finis, Mathématiques et Applications, 7, Ellipses-Edition Marketing. Zbl0847.65078
14. [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. Zbl0362.65089MR483555
15. [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. Zbl0875.65090MR1115239
16. [16] A. WEISER, M. F. WEELER1988, On convergence of block-centered finite differences for elliptic problems, SIAM J. Numer. Anal., 25, pp.351-375. Zbl0644.65062MR933730

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