Theoretical Analysis of Nedelec's Edge Elements

Japan Journal of Industrial and Applied Mathematics

Volumn 18, Issue 2, 2001, Pages 321-333

  Kikuchi, Fumio ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Discrete compactness; Electromagnetics; FEM; Nedelec's edge elements

Indexed keywords

EID: 0010648322     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03168578     Document Type: Article

References (26)

1. R.A. Adams, Sobolev Spaces. Academic Press, 1975.
2. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Meth. Appl. Sci., 21 (1998), 823-864.
3. D. Boffi, Fortin operator and discrete compactness for edge elements. Numer. Math., 87 (2000), 229-246.
4. D. Boffi, P. Fernandes, L. Gastaldi and I. Perugia, Computational models of electromagnetic resonators: analysis of edge element approximation. SIAM J. Numer. Anal., 36 (1999), 1264-1290.
5. A. Bossavit, Computational Electromagnetism: Variational Formulations, Complementary, Edge Elements. Academic Press, 1998.
6. C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, 1994.
7. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, 1991.
8. S. Caorsi, P. Fernandes and M. Raffetto, On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems. SIAM J. Numer. Anal., 38 (2000), 580-607.
9. S. Caorsi, P. Fernandes and M. Raffetto, Approximation of electromagnetic eigenproblems: a general proof of convergence for edge finite elements of any order of both Nedelec's families. CNR-IMA, Technical Report No. 16/99, Genova, Italy, 1999.
10. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, 1978.
11. M. Costabel and M. Dauge, Maxwell and Lamé eigenvalues on polyhedra. Math. Meth. Appl. Sci., 22 (1999), 243-258.
12. G. Duvault and J.-L. Lions, Inequalities in Mechanics and Physics. Springer-Verlag, 1976.
13. J. Descloux, N. Nassif and J. Rappaz, On spectral approximation. Part 2. Error estimates for the Galerkin method. RAIRO, Analyse Numerique, 12 (1978), 113-119.
14. P. Fernandes and M. Raffetto, The question of spurious modes revisited. Int. Compumag Soc. Newsletter, 7, No.1 (2000), 5-8.
15. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, 1986.
16. P. Joly, C. Poirier, J.E. Robert and P. Trouve, A new nonconforming finite element method for the computation of electromagnetic guided waves I: mathematical analysis. SIAM J. Numer. Anal., 33 (1996), 1494-1525.
17. F. Kikuchi, Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism. Computer Meth. Appl. Mech. Engng., 64 (1987), 509-521.
18. F. Kikuchi, On a discrete compactness property for the Nedelec finite elements. J. Fac. Sci., Univ. Tokyo, Sect. IA Math., 36 (1989), 479-490.
19. F. Kikuchi, Weak formulations for finite element analysis of an electromagnetic eigenvalue problem. Sci. Papers of Coll. Arts & Sci., The Univ. Tokyo, 38 (1988), 43-67.
20. F. Kikuchi, Discrete compactness of the linear rectangular Nedelec element. Abstracts of Presentations at 1999 Spring Meeting of Math. Soc. Japan, 1999, 108-111.
21. F. Kikuchi, Theoretical aspects of Nedelec's edge elements applied to electromagnetic problems. ICIAM '99. Proceedings of the 4th International Congress on Industrial and Applied Mathematics (eds. J.M. Ball and J.C.R. Hunt), Oxford University Press, 2000.
22. F. Kikuchi and M. Fukuhara, An iterative method for finite element analysis of magnetostatic problems. Advances in Numerical Mathematics (eds. T. Ushijima, Z.-C. Shi and T. Kako), Kinokuniya, 1995, 93-105.
23. F. Kikuchi, M. Yamamoto and H. Fujio, Theoretical and computational aspects of Nedelec's edge elements for electromagnetics. Computational Mechanics - New Trends and Applications (eds. E. On̄ate and S.R. Idelsohn), ©CIMNE, Barcelona, Spain, 1998.
24. 3. Numer. Math., 35 (1980), 315-341.
25. 3. Numer. Math., 50 (1986), 57-81.
26. P.P. Silvester and R.L. Ferrari, Finite Elements for Electrical Engineers (3rd edn.). Cambridge Univ. Press, 1996.