Free access
Issue
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
Page(s) 1001 - 1020
DOI http://dx.doi.org/10.1051/m2an:2007049
Published online 15 December 2007
  1. M. Ainsworth, Dispersive properties of high order Nédélec/edge element approximation of the time-harmonic Maxwell equations. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 362 (2004) 471–491. [CrossRef] [MathSciNet]
  2. M. Ainsworth and J. Coyle, Hierarchic finite element bases on unstructured tetrahedral meshes. Int. J. Numer. Meth. Engng. 58 (2003) 2103–2130. [CrossRef]
  3. M. Ainsworth, J. Coyle, P.D. Ledger and K. Morgan, Computation of Maxwell eigenvalues using higher order edge elements in three-dimensions. IEEE Trans. Magn. 39 (2003) 2149–2153. [CrossRef]
  4. M.A. Armstrong, Basic Topology. Springer-Verlag, New York (1983).
  5. D. Arnold, R. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [CrossRef] [MathSciNet]
  6. D. Boffi, M. Costabel, M. Dauge and L.F. Demkowicz, Discrete compactness for the hp version of rectangular edge finite elements. ICES Report 04–29 (2004).
  7. A. Bossavit, Computational Electromagnetism. Academic Press, New York (1998).
  8. A. Bossavit, Generating Whitney forms of polynomial degree one and higher. IEEE Trans. Magn. 38 (2002) 341–344. [CrossRef]
  9. A. Bossavit and F. Rapetti, Whitney forms of higher degree. Preprint.
  10. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations. Springer-Verlag, Berlin (1986).
  11. J. Gopalakrishnan, L.E. Garcia-Castillo and L.F. Demkowicz, Nédélec spaces in affine coordinates. ICES Report 03–48 (2003).
  12. R.D. Graglia, D.R. Wilton and A.F. Peterson, Higher order interpolatory vector bases for computational electromagnetics. IEEE Trans. on Ant. and Propag. 45 (1997) 329–342. [CrossRef]
  13. R. Hiptmair, Canonical construction of finite elements. Math. Comp. 68 (1999) 1325–1346. [CrossRef] [MathSciNet]
  14. R. Hiptmair, High order Whitney forms. Prog. Electr. Res. (PIER) 32 (2001) 271–299. [CrossRef]
  15. G.E. Karniadakis and S.J. Sherwin, Spectral hp element methods for CFD. Oxford Univ. Press, London (1999).
  16. J.M. Melenk, On condition numbers in hp-FEM with Gauss-Lobatto-based shape functions. J. Comput. Appl. Math. 139 (2002) 21–48. [CrossRef] [MathSciNet]
  17. P. Monk, Finite Element Methods for Maxwell's Equations. Oxford University Press (2003).
  18. J.C. Nédélec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet]
  19. F. Rapetti and A. Bossavit, Geometrical localization of the degrees of freedom for Whitney elements of higher order. IEE Sci. Meas. Technol. 1 (2007) 63–66. [CrossRef]
  20. J. Schöberl and S. Zaglmayr, High order Nédélec elements with local complete sequence properties. COMPEL 24 (2005) 374–384. [CrossRef] [MathSciNet]
  21. J. Stillwell, Classical topology and combinatorial group theory, Graduate Text in Mathematics 72. Springer-Verlag (1993).
  22. J.P. Webb and B. Forghani, Hierarchal scalar and vector tetrahedra. IEEE Trans. on Magn. 29 (1993) 1495–1498. [CrossRef]
  23. H. Whitney, Geometric integration theory. Princeton Univ. Press (1957).

Recommended for you