Free Access
Issue
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
Page(s) 1203 - 1249
DOI https://doi.org/10.1051/m2an:2005047
Published online 15 November 2005
  1. G. Acosta and R.G. Durán, The maximum angle condition for mixed and nonconforming elements: application to the Stokes equations. SIAM J. Numer. Anal. 37 (1999) 18–36. [CrossRef] [MathSciNet] [Google Scholar]
  2. I. Babuška and A.K. Aziz, On the angle condition in the finite element method. SIAM J. Numer. Anal. 13 (1976) 214–226. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Baranger, J.-F. Maitre and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal Numér. 30 (1996) 445–465. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  4. S. Boivin, F. Cayré and J.-M. Hérard, A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes. Int. J. Therm. Sci. 39 (2000) 806–825. [CrossRef] [Google Scholar]
  5. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis Vol. 2, P.G. Ciarlet and J.-L. Lions, Eds., Amsterdam North-Holland/Elsevier (1991) 17–351. [Google Scholar]
  6. Y. Coudière, J.-P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. ESAIM: M2AN 33 (1999) 493–516. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  7. Y. Coudière and P. Villedieu, Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes. ESAIM: M2AN 34 (2000) 1123–1149. [CrossRef] [EDP Sciences] [Google Scholar]
  8. K. Domelevo and P. Omnes, Construction et analyse numérique d'une méthode de volumes finis pour l'équation de Laplace sur des maillages bidimensionnels presque quelconques (in French), Rapport CEA (2004). [Google Scholar]
  9. R. Eymard, T. Gallouët and R. Herbin, Handbook of Numerical Analysis Vol. 7, P.G. Ciarlet and J.-L. Lions, Eds., North-Holland/Elsevier, Amsterdam (2000) 713–1020. [Google Scholar]
  10. R. Eymard, T. Gallouët and R. Herbin, Finite volume approximation of elliptic problems and convergence of an approximate gradient. Appl. Numer. Math. 37 (2001) 31–53. [CrossRef] [MathSciNet] [Google Scholar]
  11. I. Faille, A control volume method to solve an elliptic equation on a two-dimensional irregular meshing. Comput. Methods Appl. Mech. Engrg. 100 (1991) 275–290. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Gallouët, R. Herbin and M.-H. Vignal, Error estimates for the approximate finite volume solution of convection diffusion equations with general boundary conditions. SIAM J. Numer. Anal. 37 (2000) 1935–1972. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Glowinski, J. He, J. Rappaz and J. Wagner, A multi-domain method for solving numerically multi-scale elliptic problems. C. R. Acad. Sci. Paris Ser. I Math 338 (2004) 741–746. [Google Scholar]
  14. R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods Partial Differential Equations 11 (1995) 165–173. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160 (2000) 481–499. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.M. Hyman and M. Shashkov, Adjoint operators for the natural discretizations of the divergence, gradient, and curl on logically rectangular grids. Appl. Numer. Math. 25 (1997) 413–442. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.M. Hyman and M. Shashkov, Natural discretizations for the divergence, gradient, and curl on logically rectangular grids. Comput. Math. Appl. 33 (1997) 81–104. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  18. P. Jamet, Estimations d'erreur pour des éléments finis droits presque dégénérés. RAIRO Anal. numér. 10 (1976) 43–61. [Google Scholar]
  19. L. Klinger, J.B. Vos and K. Appert, A simplified gradient evaluation on non-orthogonal meshes; application to a plasma torch simulation method. Comput. Fluids 33 (2004) 643–654. [Google Scholar]
  20. I.D. Mishev, Finite volume methods on Voronoi meshes. Numer. Methods Partial Differential Equations 14 (1998) 193–212. [CrossRef] [MathSciNet] [Google Scholar]
  21. L.E. Payne and H.F. Weinberger, An optimal Poincaré inequality for convex domains. Arch. Rational Mech. Anal. 5 (1960) 286–292. [CrossRef] [MathSciNet] [Google Scholar]
  22. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical aspects of the finite element method, I. Galligani and E. Magenes, Eds., Springer-Verlag, New-York. Lecture Notes in Math. 606 (1977) 292–315. [CrossRef] [Google Scholar]
  23. L. Saas, I. Faille, F. Nataf and F. Willien, Domain decomposition for a finite volume method on non-matching grids. C. R. Acad. Sci. Paris Ser. I Math. 338 (2004) 407–412. [Google Scholar]
  24. G. Strang, Variational crimes in the finite element method, in The mathematical foundations of the finite element method with applications to partial differential equations, A.K. Aziz Ed., Academic Press, New York (1972) 689–710. [Google Scholar]
  25. R. Vanselow and H.P. Scheffler, Convergence analysis of a finite volume method via a new nonconforming finite element method. Numer. Methods Partial Differential Equations 14 (1998) 213–231. [CrossRef] [MathSciNet] [Google Scholar]
  26. Special issue on the simulation of transport around a nuclear waste disposal site: the Couplex test cases. Computat. Geosci. 8 (2004). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you