EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 40 / No 2 (March-April 2006) ESAIM: M2AN, 40 2 (2006) 367-391 References
Free Access
Issue
ESAIM: M2AN
Volume 40, Number 2, March-April 2006
Page(s) 367 - 391
DOI https://doi.org/10.1051/m2an:2006013
Published online 21 June 2006
  1. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods. SIAM J. Sci. Comput. 19 (1998) 1700–1716. [CrossRef] [MathSciNet] [Google Scholar]
  2. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, Discretization on unstructured grids for inhomogeneous, anisotropic media. Part II: Discussion and numerical results. SIAM J. Sci. Comput. 19 (1998) 1717–1736. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Aftosmis, D. Gaitonde and T. Sean Tavares, On the accuracy, stability and monotonicity of various reconstruction algorithms for unstructured meshes. AIAA (1994), paper No. 94-0415. [Google Scholar]
  4. A. Agouzal, J. Baranger, J.-F. Maître and F. Oudin, Connection between finite volume and mixed finite element methods for a diffusion problem with nonconstant coefficients. Application to a convection diffusion problem. East-West J. Numer. Math. 3 (1995) 237–254. [MathSciNet] [Google Scholar]
  5. T. Arbogast, M.F. Wheeler and N. Zhang, A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J. Numer. Anal. 33 (1996) 1669–1687. [CrossRef] [MathSciNet] [Google Scholar]
  6. T. Arbogast, M.F. Wheeler and I. Yotov, Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal. 34 (1997) 828–852. [CrossRef] [MathSciNet] [Google Scholar]
  7. T. Arbogast, C.N. Dawson, P.T. Keenan, M.F. Wheeler and I. Yotov, Enhanced cell-centered finite differences for elliptic equations on general geometry. SIAM J. Sci. Comput. 19 (1998) 404–425. [Google Scholar]
  8. D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. RAIRO Modél. Math. Anal. Numér. 19 (1985) 7–32. [Google Scholar]
  9. J. Baranger, J.-F. Maître and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal. Numér. 30 (1996) 445–465. [Google Scholar]
  10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). [Google Scholar]
  11. F. Brezzi, J. Douglas Jr. and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Brezzi, J. Douglas Jr., R. Duran and M. Fortin, Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51 (1987) 237–250. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Chavent, A. Younès and Ph. Ackerer, On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles. Comput. Methods Appl. Mech. Engrg. 192 (2003) 655–682. [Google Scholar]
  14. Z. Chen, Equivalence between and multigrid algorithms for nonconforming and mixed methods for second-order elliptic problems. East-West J. Numer. Math. 4 (1996) 1–33. [MathSciNet] [Google Scholar]
  15. Y. Coudière, J.-P. Vila and Villedieu Ph., 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]
  16. C. Dawson, Analysis of an upwind-mixed finite element method for nonlinear contaminnat transport equations. SIAM J. Numer. Anal. 35 (1998) 1709–1724. [CrossRef] [MathSciNet] [Google Scholar]
  17. C. Dawson and V. Aizinger, Upwind-mixed methods for transport equations. Comput. Geosci. 3 (1999) 93–110. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Douglas Jr. and J.E. Roberts, Global estimates for mixed methods for second order elliptic equations. Math. Comp. 44 (1985) 39–52. [CrossRef] [MathSciNet] [Google Scholar]
  19. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of Numerical Analysis, Ph.G. Ciarlet and J.-L. Lions Eds. Elsevier Science B.V., Amsterdam 7 (2000) 713–1020. [Google Scholar]
  20. R. Eymard, T. Gallouët and R. Herbin, A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension. IMA J. Numer. Anal. 26 (2006) 326–353. [CrossRef] [MathSciNet] [Google Scholar]
  21. I. Faille, A control volume method to solve an elliptic equation on a two-dimensional irregular mesh. Comput. Methods Appl. Mech. Engrg. 100 (1992) 275–290. [Google Scholar]
  22. J.R. Gilbert, C. Moler and R. Schreiber, Sparse matrices in MATLAB: Design and implementation. SIAM J. Matrix Anal. Appl. 13 (1992) 333–356. [CrossRef] [MathSciNet] [Google Scholar]
  23. M.R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand. 49 (1952) 409–436. [Google Scholar]
  24. H. Hoteit, J. Erhel, R. Mosé, B. Philippe and Ph. Ackerer, Numerical reliability for mixed methods applied to flow problems in porous media. Comput. Geosci. 6 (2002) 161–194. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Jaffré, Éléments finis mixtes et décentrage pour les équations de diffusion-convection. Calcolo 23 (1984) 171–197. [Google Scholar]
  26. L. Jeannin, I. Faille and T. Gallouët, Comment modéliser les écoulements diphasiques compressibles sur des grilles hybrides ? Oil & Gas Science and Technology – Rev. IFP 55 (2000) 269–279. [CrossRef] [EDP Sciences] [Google Scholar]
  27. R.A. Klausen and G.T. Eigestad, Multi point flux approximations and finite element methods; practical aspects of discontinuous media, Proc. 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, B003 (2004). [Google Scholar]
  28. R.A. Klausen and T.F. Russell, Relationships among some locally conservative discretization methods which handle discontinuous coefficients. Comput. Geosci. 8 (2004) 341–377. [CrossRef] [MathSciNet] [Google Scholar]
  29. L.D. Marini, An inexpensive method for the evaluation of the solution of the lowest order Raviart–Thomas mixed method. SIAM J. Numer. Anal. 22 (1985) 493–496. [CrossRef] [MathSciNet] [Google Scholar]
  30. J.C. Nédélec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin (1994). [Google Scholar]
  32. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for 2-nd order elliptic problems, in Mathematical Aspects of Finite Element Methods. Galligani I., Magenes E. Eds., Lect. Notes Math., Springer, Berlin 606 (1977) 292–315. [Google Scholar]
  33. J.E. Roberts and J.-M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis, Ph.G. Ciarlet and J.-L. Lions Eds., Elsevier Science B.V., Amsterdam 2 (1991) 523–639. [Google Scholar]
  34. T.F. Russell and M.F. Wheeler, Finite element and finite difference methods for continuous flows in porous media, in The Mathematics of Reservoir Simulation, R.E. Ewing Ed., SIAM, Philadelphia (1983) 35–106. [Google Scholar]
  35. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Publishing Company (1996). [Google Scholar]
  36. H.A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (1992) 631–644. [CrossRef] [MathSciNet] [Google Scholar]
  37. M. Vohralík, Equivalence between mixed finite element and multi-point finite volume methods. C. R. Acad. Sci. Paris., Ser. I 339 (2004) 525–528. [Google Scholar]
  38. M. Vohralík, Equivalence between mixed finite element and multi-point finite volume methods. Derivation, properties, and numerical experiments, in Proceedings of ALGORITMY 2005, Slovak University of Technology, Slovakia (2005) 103–112. [Google Scholar]
  39. A. Younès, R. Mose, Ph. Ackerer and G. Chavent, A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J. Comput. Phys. 149 (1999) 148–167. [CrossRef] [MathSciNet] [Google Scholar]
  40. A. Younès, Ph. Ackerer and G. Chavent, From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions. Internat. J. Numer. Methods Engrg. 59 (2004) 365–388. [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