Numerical analysis of relaxed micromagnetics by penalised finite elements

Numerische Mathematik

Volumn 90, Issue 1, 2001, Pages 65-99

  Carstensen, Carsten ^a   Prohl, Andreas ^a  

^a UNIVERSITY OF KIEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035526468     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100268     Document Type: Article

References (23)

1. [ACF] J. Alberty, C. Carstensen, S.A. Funken, Remarks around 50 lines of Matlab: Finite Element implementation, Numerical Algorithms (1999) Accepted, and: Berichtsreihe des Mathematischen Seminars Kiel 98-11 (1998) (http://www.numerik.uni-kiel.de/reports/1998/98-11.html)
2. [AF] D. N. Arnold, R. S. Falk, A uniformly accurate finite element method for the Mindlin-Reissner plate, SIAM J. Numer. Anal. 26 (1989), 1276-1290
3. [BBF] F. Brezzi, K.-J. Bathe, M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates. Int. J. Num. Meth. Eng. 28 (1989), 1787-1801
4. [BF] F. Brezzi, M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, 1991
5. [BS] S.C. Brenner, L.R. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics 15, Springer-Verlag, New York, 1994
6. [B] W.F. Brown, Micromagnetics, Interscience, New York, 1963
7. C. Carstensen, Petr Plecháč, Numerical solution of the scalar double-well problem allowing microstructure, Math. Comp. 66 (1997), 997-1026
8. C. Carstensen, Petr Plecháč, Numerical Analysis of Compatible Phase Transitions in Elastic Solids, SIAM J. Numer. Anal. 37 (2000), 2061-2081
9. P. Clément, Approximation by finite element functions using local regularization, Sér. Rouge Anal. Numér. (RAIRO) R-2 (1975), 77-84
10. B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Math. Sciences 78, Springer-Verlag, Heidelberg, 1989
11. [ADS] A. De Simone, Energy Minimizers for Large Ferromagnetic Bodies, Arch. Rat. Mech. Anal. 125 (1993), 99-143
12. [GR] V. Girault, P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986
13. [HS] A. Hubert, R. Schäfer, Magnetic Domains - The Analysis of Magnetic Microstructures, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1998
14. [JK] R. D. James, D. Kinderlehrer, Frustration in ferromagnetic materials, Continuum Mech. Thermodyn. 2 (1990), 215-239
15. [KR] M. Kružík, T. Roubíček, Weierstrass-type maximum principle for microstructure in micromagnetics, Preprintreihe des des Max-Planck-Instituts für Mathematik in den Naturwissenschaften Leipzig 99-40 (1999)
16. [LM] M. B. Luskin, L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics, SIAM J. Numer. Anal. 29 (1992), 320-331
17. P. Pedregal, Parametrized Measures and Variational Principles, Birkhäuser, 1997
18. P. Pedregal, Numerical computation of parametrized measures, Numer. Funct. Anal. Opt. 16 (1995), 1049-1066
19. P. Pedregal, On the numerical analysis of nonconvex variational problems, Num. Math. 74 (1996), 325-336
20. [Pr] A. Prohl, Error analysis for the computation of microstructure in uniaxial ferromagnets, Berichtsreihe des Mathematischen Seminars Kiel 98-33 (1999) (http://www.numerik.uni-kiel.de/reports/1998/98-33.html)
21. [R] T. Roubíček, Relaxation in Optimization Theory and Variational Calculus, W. de Gruyter, Berlin-New York, 1997
22. [T] L. Tartar, Beyond Young Measures, Meccanica 30 (1995), 505-526
23. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques, Wiley-Teubner, 1996