Connection between finite volume and mixed finite element methods

Jacques Baranger; Jean-François Maitre; Fabienne Oudin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 4, page 445-465
  • ISSN: 0764-583X

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Baranger, Jacques, Maitre, Jean-François, and Oudin, Fabienne. "Connection between finite volume and mixed finite element methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.4 (1996): 445-465. <http://eudml.org/doc/193811>.

@article{Baranger1996,
author = {Baranger, Jacques, Maitre, Jean-François, Oudin, Fabienne},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element method; finite volume method; Laplace equation; Raviart-Thomas element; error bounds},
language = {eng},
number = {4},
pages = {445-465},
publisher = {Dunod},
title = {Connection between finite volume and mixed finite element methods},
url = {http://eudml.org/doc/193811},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Baranger, Jacques
AU - Maitre, Jean-François
AU - Oudin, Fabienne
TI - Connection between finite volume and mixed finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 4
SP - 445
EP - 465
LA - eng
KW - mixed finite element method; finite volume method; Laplace equation; Raviart-Thomas element; error bounds
UR - http://eudml.org/doc/193811
ER -

References

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  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

Citations in EuDML Documents

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  1. Yves Coudière, Jean-Paul Vila, Philippe Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
  2. Reiner Vanselow, Convergence analysis for an exponentially fitted finite volume method
  3. B. Courbet, J. P. Croisille, Finite volume box schemes on triangular meshes
  4. Reiner Vanselow, Convergence analysis for an exponentially fitted Finite Volume Method
  5. Yves Coudière, Philippe Villedieu, Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
  6. Komla Domelevo, Pascal Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
  7. Paola Causin, Riccardo Sacco, Carlo L. Bottasso, Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
  8. Komla Domelevo, Pascal Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
  9. Paola Causin, Riccardo Sacco, Carlo L. Bottasso, Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
  10. Yves Coudière, Philippe Villedieu, Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes

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