Free access
Issue
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
Page(s) 941 - 959
DOI http://dx.doi.org/10.1051/m2an:2008030
Published online 30 July 2008
  1. D.N. Arnold, Differential complexes and numerical stability, in Proceedings of the International Congress of Mathematicians, Vol. I, Higher Ed. Press, Beijing (2002) 137–157.
  2. M. Berndt, K. Lipnikov, D. Moulton and M. Shashkov, Convergence of mimetic finite difference discretizations of the diffusion equation. East-West J. Numer. Math 9 (2001) 253–316. [CrossRef] [MathSciNet]
  3. P. Bochev and J.M. Hyman, Principles of mimetic discretizations of differential operators, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA Volumes in Mathematics and its Applications 142, Springer, New York (2006).
  4. A. Bossavit, Generating whitney forms of polynomial degree one and higher. IEEE Trans. Magn. 38 (2002) 341–344. [CrossRef]
  5. R. Hiptmair, Canonical construction of finite elements. Math. Comp. 68 (1999) 1325–1346. [CrossRef] [MathSciNet]
  6. A. Hirani, Discrete Exterior Calculus. Ph.D. thesis, California Institute of Technology, USA (2003).
  7. J.M. Hyman and M. Shashkov, The adjoint operators for the natural discretizations for the divergence, gradient, and curl on logically rectangular grids. IMACS J. Appl. Num. Math. 25 (1997) 1–30.
  8. 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]
  9. J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comp. Phys. 151 (1999) 881–909. [CrossRef] [MathSciNet]
  10. J.M. Hyman and M. Shashkov, The orthogonal decomposition theorems for mimetic finite difference methods. SIAM J. Numer. Anal. 36 (1999) 788–818. [CrossRef] [MathSciNet]
  11. J.C. Nedelec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet]
  12. J.C. Nedelec, A new family of mixed finite elements in Formula . Numer. Math. 50 (1986) 57–81. [CrossRef] [MathSciNet]
  13. R.A. Nicolaides, Direct discretization of planar div-curl problems. SIAM J. Numer. Anal. 29 (1992) 32–56. [CrossRef] [MathSciNet]
  14. R. Nicolaides and K. Trapp, Covolume discretizations of differential forms, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA Volumes in Mathematics and its Applications 142, Springer, New York (2006).
  15. R.A. Nicolaides and D.Q. Wang, Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions. Math. Comp. 67 (1998) 947–963. [CrossRef] [MathSciNet]
  16. R.A. Nicolaides and X. Wu, Covolume solutions of three-dimensional div-curl equations. SIAM J. Numer. Anal. 34 (1997) 2195–2203. [CrossRef] [MathSciNet]
  17. P.A. Raviart and J.M. Thomas, A mixed finite elemnt method for second order elliptic problems, in Springer Lecture Notes in Mathematics 606, Springer-Verlag (1977) 292–315.
  18. K. Trapp, A Class of Compatible Discretizations with Applications to Div-Curl Systems. Ph.D. thesis, Carnegie Mellon University, USA (2004).

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