Free Access
Issue
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
Page(s) 123 - 147
DOI https://doi.org/10.1051/m2an:2006001
Published online 23 February 2006
  1. T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for second order elliptic problems. Math. Comp. 64 (1995) 943–972. [MathSciNet] [Google Scholar]
  2. T. Arbogast, M. 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]
  3. 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. [MathSciNet] [Google Scholar]
  4. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749–1779. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267–279. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag (1991). [Google Scholar]
  8. F. Brezzi, J. Douglas 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]
  9. F. Brezzi, J. Douglas, R. Durán and M. Fortin, Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51 (1987) 237–250. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Brezzi, J. Douglas, M. Fortin and L.D. Marini, Efficient rectangular mixed finite elements in two and three variables. RAIRO Modél. Math. Anal. Numér. 21 (1987) 581–604. [MathSciNet] [Google Scholar]
  11. F. Brezzi, G. Manzini, L.D. Marini, P. Pietra and A. Russo, Discontinuous Galerkin approximations for elliptic problems. Numer. Methods Partial Differential Equations 16 (2000) 365–378. [CrossRef] [MathSciNet] [Google Scholar]
  12. Z. Cai, J.E. Jones, S.F. McCormick and T.F. Russell, Control-volume mixed finite element Methods. Comput. Geosci. 1 (1997) 289–315. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  13. P. Castillo, B. Cockburn, I. Perugia and D. Schötzau, An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 38 (2000) 1676–1706. [CrossRef] [MathSciNet] [Google Scholar]
  14. Z. Chen, Expanded mixed finite element methods for linear second-order elliptic problems I. RAIRO Modél. Math. Anal. Numér. 32 (1998) 479–499. [MathSciNet] [Google Scholar]
  15. Z. Chen, On the relationship of various discontinuous finite element methods for second-order elliptic equations. East-West J. Numer. Math. 9 (2001) 99–122. [MathSciNet] [Google Scholar]
  16. Z. Chen and J. Douglas, Prismatic mixed finite elements for second order elliptic problems. Calcolo 26 (1989) 135–148. [CrossRef] [MathSciNet] [Google Scholar]
  17. S.H. Chou and P.S. Vassilevski, A general mixed covolume framework for constructing conservative schemes for elliptic problems. Math. Comp. 68 (1999) 991–1011. [CrossRef] [MathSciNet] [Google Scholar]
  18. S.H. Chou, D.Y. Kwak and P. Vassilevski, Mixed covolume methods for elliptic problems on triangular grids. SIAM J. Numer. Anal. 35 (1998) 1850–1861. [CrossRef] [MathSciNet] [Google Scholar]
  19. S.H. Chou, D.Y. Kwak and K.Y. Kim, A general framework for constructing and analyzing mixed finite volume methods on quadrilateral grids: the overlapping covolume case. SIAM J. Numer. Anal. 39 (2001) 1170–1196 [CrossRef] [MathSciNet] [Google Scholar]
  20. S.H. Chou, D.Y. Kwak and K.Y. Kim, Mixed finite volume methods on non-staggered quadrilateral grids for elliptic problems. Math. Comp. 72 (2003) 525–539. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland (1978). [Google Scholar]
  22. B. Cockburn and C.W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion system. SIAM J. Numer. Anal. 35 (1998) 2440–2463. [CrossRef] [MathSciNet] [Google Scholar]
  23. B. Courbet and J.P. Croisille, Finite volume box schemes on triangular meshes. RAIRO Modél. Math. Anal. Numér. 32 (1998) 631–649. [MathSciNet] [Google Scholar]
  24. J.P. Croisille, Finite volume box schemes and mixed methods ESAIM: M2AN 34 (2000) 1087–1106. [Google Scholar]
  25. J.P. Croisille and I. Greff, Some nonconforming mixed box schemes for elliptic problems. Numer. Methods Partial Differential Equations 18 (2002) 355–373. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Dawson, The Formula local discontinuous Galerkin method for elliptic equations. SIAM J. Numer. Anal. 40 (2002) 2151–2170. [CrossRef] [MathSciNet] [Google Scholar]
  27. R.G. Durán, Error analysis in Formula , for mixed finite element methods for linear and quasi-linear elliptic problems. RAIRO Modél. Math. Anal. Numér. 22 (1988) 371–387. [MathSciNet] [Google Scholar]
  28. R.S. Falk and J.E. Osborn, Error estimates for mixed methods. RAIRO Anal. Numér. 14 (1980) 249–277. [MathSciNet] [Google Scholar]
  29. X. Feng and O.A. Karakashian, Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1343–1365. [CrossRef] [MathSciNet] [Google Scholar]
  30. J. Gopalakrishnan and G. Kanschat, A multilevel discontinuous Galerkin method. Numer. Math. 95 (2003) 527–550. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Micheletti and R. Sacco, Dual-primal mixed finite elements for elliptic problems. Numer. Methods Partial Differential Equations 17 (2001) 137–151. [CrossRef] [MathSciNet] [Google Scholar]
  32. J.C. Nedelec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  33. J.C. Nedelec, A new family of mixed finite elements in Formula . Numer. Math. 50 (1986) 57–81. [CrossRef] [MathSciNet] [Google Scholar]
  34. I. Perugia and D. Schötzau, An hp-analysis of the local discontinuous Galerkin method for diffusion problems. J. Sci. Comput. 17 (2002) 561–571. [CrossRef] [MathSciNet] [Google Scholar]
  35. P.A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Proc. Conference on Mathematical Aspects of Finite Element Methods, Springer-Verlag. Lect. Notes Math. 606 (1977) 292–315. [CrossRef] [Google Scholar]
  36. B. Riviere, M.F. Wheeler and V. Girault, A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39 (2001) 902–931. [CrossRef] [MathSciNet] [Google Scholar]
  37. J.E. Roberts and J.M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis, Vol. II, North-Holland (1991) 523–639. [Google Scholar]
  38. R. Sacco and F. Saleri, Mixed finite volume methods for semiconductor device simulation. Numer. Methods Partial Differential Equations 13 (1997) 215–236. [CrossRef] [MathSciNet] [Google Scholar]
  39. A. Weiser and M.F. Wheeler, On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal. 25 (1988) 351–375. [CrossRef] [MathSciNet] [PubMed] [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