An adaptive finite element method for the H - ψ formulation of time-dependent eddy current problems

Numerische Mathematik

Volumn 103, Issue 4, 2006, Pages 667-689

  Zheng, Weiying ^a   Chen, Zhiming ^a   Wang, Long ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744758948     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-006-0008-3     Document Type: Article

References (34)

1. Ammari, H., Buffa, A., Nédélec, J.C.: A justification of eddy current model for the maxwell equations. SIAM J Appl Math 60, 1805-1823 (2000)
2. Amrouche, C., Bernardi, C., Dauge, M., Girault, V.: Vector potentials in three-dimensional non-smooth domains. Math Methods Appl Sci 21, 823-864 (1998)
3. Babuška, I., Rheinboldt, C.: Error estimates for adaptive finite element computations. SIAM J Numer Anal 15, 736-754 (1978)
4. Beck, R., Hiptmar, R., Hoppe, R.H.W., Wohlmoth, B.: Residual based a posteriori error estimations for eddy current computation. M2AN Math Model Numer Anal 34, 159-182 (2000)
5. Beck, R., Hiptmar, R., Wohlmoth, B.: Hierarchical error estimator for eddy current computation. In: Neittaanmäki, P., Tiihonen, T. (eds.) ENUMATH 99-Proceedings of the 3rd European Conference on numerical mathematics and advanced applications, Jyväskylä, Finland, July 26-30, 2000, pp. 110-120 World Scientific, Singapore, 2000
6. 2-Theory of the Maxwell operator in arbitary domains. Usp Mat Nauk 42, 61-76 (1987) (in Russian);
7. RussMath Surv 43, 75-96 (1987) (in English)
8. Bossavit, A.: Computational electromagnetism, variational formulations, edge elements, complementarity. Academic, Boston (1998)
9. Bouillault, F., Ren, Z., Razek, A.: Calculation of eddy currents in an asymmetrical conductor with a hole. COMPEL 9(Supple A), 227-229 (1990)
10. Chen, Z., Dai, S.: Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity. SIAM J Numer Anal 38, 1961-1985 (2001)
11. Chen, Z., Dai, S.: On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients. SIAM J Sci Comput 24, 443-462 (2002)
12. Chen, Z., Jia, F.: An adaptive finite element method with reliable and efficient error control for linear parabolic problems. Math Comput 73, 1163-1197 (2004)
13. Chen, Z., Wu, H.: An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures. SIAM J Numer Anal 41, 799-826 (2003)
14. Chen, Z., Nochetto, R.H., Schmidt, A.: An adaptive finite element method with error control for the continuous casting problem. Comput Methods Appl Mech Eng 189, 249-276 (2000)
15. Chen, Z., Wang, L., Zheng, W.: An adaptive multilevel method for time-harmonic maxwell equations with singularities. Research Report, Institute of Computational Mathematics, Chinese Academy of Sciences (2006)
16. Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North-Holland (1978)
17. Clemens, M., Weiland, T.: Transient eddy-current calculations with the FI-method. IEEE Trans Magn 35, 1163-1166 (1999)
18. Costabel, M., Dauge, M., Nicaise, S.: Singularities of eddy current problems. ESAIM: Math Model Numer Anal 37, 807-831 (2003)
19. Dhia, A.B., Hazard, C., Lohrengel, S.: A singular field method for the solution of Maxwell's equations in polyhedral domains. SIAM J Appl Math 59, 2028-2044 (1999)
20. Dular, P., Henrotte, F., Robert, F., Genon, A., Legros, W.: A generalized source magnetic field calculation method for inductors of any shape. IEEE Trans Magn 33, 1398-1401 (1997)
21. Fujiwara, K., Nakata, T.: Results for benchmark problem 7 (a symmetrical conductor with a hole). COMPEL 9, 137-154 (1990)
22. Girault, V., Raviart, P.A.: Finite element methods for Naviar-Stokes equations, theory and algorithms. Berlin Heidelberg New York: Springer 1986
23. Hiptmair, R.: Analysis of multilevel methods for eddy current problems. Math Comput 72, 1-23 (2002)
24. Li, K., Ma, Y.: Hilbert-space methods for partial differential equations in mathematical physics (I) (in Chinese). Xi'an (China): Xi'an Jiaotong University press 1990
25. Monk, P.: A posteriori error indicators for Maxwell's equations. J Comp Appl Math 100, 173-190 (1998)
26. Morin, P., Nochetto, R.H., Siebert, K.G.: Data oscillations and convergence of adaptive FEM. SIAM J Numer Anal 38, 466-488 (2000)
27. 3. Numer Math 35, 315-341 (1980)
28. Pasciak, J.E., Zhao, J.: Overlapping Schwartz methods in H(curl) on polyhedral domains. East West J Numer Math 10, 221-234 (2002)
29. Schmidt, A., Siebert, K.G.: ALBERT - An adaptive hierarchical finite element toolbox, the new version ALBERTA is available online from http://www.alberta-fem.de
30. Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math Comput 54, 483-493 (1990)
31. Stein, E.M.: Singular integrals and differetiability properties of functions. Princeton: Princeton University Press 1970
32. Stephan, E., Maischak, M.: A posteriori error estimate for fem-bem couplings of three-dimensional electromagnetic problems. Report IFAM 72, Institut für Angewandte Mathematik, Universität Hannover, Hannover, Germany 2003
33. 3. Report IFAM 53, Institut für Angewandte Mathematik, Universität Hannover, Hannover, Germany 2003
34. Verfürth, R.: A review of a posteriori error estimation and adaptive mesh-refinement rechniques. Chichester (Stuttgart): Wiley 1996