Error estimates for Landau-Lifshitz-Gilbert equation with magnetostriction

Applied Numerical Mathematics

Volumn 56, Issue 8, 2006, Pages 1019-1039

  Baňas, L'ubomír ^a   Slodička, Marián ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

A posteriori error estimates; A priori error estimates; Ferromagnetism; Magnetostriction; Numerical methods

Indexed keywords

ADAPTIVE ALGORITHMS; ERROR ANALYSIS; FERROMAGNETIC MATERIALS; MAGNETIZATION; NUMERICAL METHODS;

A POSTERIORI ERROR ESTIMATES; A PRIORI ERROR ESTIMATES; DISCRETIZATION; LIFSHITZ-GILBERT EQUATION;

MAGNETOSTRICTION;

EID: 33744538994     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2005.09.003     Document Type: Article

References (29)

1. Anzellotti G., Baldo S., and Visintin A. Asymptotic behavior of the Landau-Lifshitz model of ferromagnetism. Appl. Math. Optimization 23 3 (1991) 171-192
2. Baňas L.'. A numerical method for the Landau-Lifshitz equation with magnetostriction. Math. Methods Appl. Sci. 15 16 (2005) 1939-1954
3. Baňas L.'., and Slodička M. Space discretization for the Landau-Lifshitz-Gilbert equation with magnetostriction. Comput. Methods Appl. Mech. Engrg. 194 2-5 (2005) 467-477
4. Bernardi C., and Süli E. Time and space adaptivity for the second-order wave equation. Math. Models Methods Appl. Sci. 15 2 (2005) 199-225
5. Bertsch M., Podio Guidugli P., and Valente V. On the dynamics of deformable ferromagnets. I. Global weak solutions for soft ferromagnets at rest. Ann. Mat. Pura Appl. 4 179 (2001) 331-360
6. Brenner S., and Scott L. The Mathematical Theory of Finite Element Methods (1994), Springer, Berlin
7. Brown Jr. W.F. Micromagnetics (1963), Interscience, New York
8. Brown Jr. W.F. Magnetoelastic Interactions (1966), Springer, Berlin
9. Carstensen C., and Prohl A. Numerical analysis of relaxed micromagnetics by penalised finite elements. Numer. Math. 90 1 (2001) 65-99
10. Chen Z., and Dai S. Adaptive Galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductivity. SIAM J. Numer. Anal. 38 6 (2001) 1961-1985
11. Clément P. Approximation by finite element functions using local regularization. Rev. Franc. Automat. Inform. Rech. Operat. 9 R-2 (1975) 77-84
12. De Simone A. Energy minimizers for large ferromagnetic bodies. Arch. Rat. Mech. Anal. 125 2 (1993) 99-143
13. De Simone A. Magnetization and magnetostriction curves from micromagnetics. J. Appl. Phys. 76 10 (1994) 7018-7020
14. De Simone A., and James R. A constrained theory of magnetoelasticity. J. Mech. Phys. Solids 50 2 (2002) 283-320
15. Eriksson K., and Johnson C. Adaptive finite element methods for parabolic problems IV: Nonlinear problems. SIAM J. Numer. Anal. 32 6 (1995) 1729-1749
16. Gilbert T.L. A Lagrangian formulation of gyromagnetic equation of the magnetic field. Phys. Rev. 100 (1955) 1243
17. Guo B., and Ding S. Neumann problem for the Landau-Lifshitz-Maxwell system in two dimensions. Chinese Ann. Math., Ser. B 22 4 (2001) 529-540
18. Guo B., and Su F. Global weak solution for the Landau-Lifshitz-Maxwell equation in three space dimensions. J. Math. Anal. Appl. 211 1 (1997) 326-346
19. Hulbert G.M., and Hughes T.J.R. Space-time finite element methods for second-order hyperbolic equations. Comput. Methods Appl. Mech. Engrg. 84 3 (1990) 327-348
20. M. Kružík, A. Prohl, Recent Developments in Modeling, Analysis and Numerics of Ferromagnetism, IMA Preprint Series, vol. 1998, 2004
21. Landau L., and Lifshitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion 8 (1935) 153-169
22. Landau L., and Lifshitz E. Electrodynamics of Continuous Media (1960), Pergamon Press, Oxford (translated from the Russian by J.B. Sykes and J.S. Bell), x+417 p
23. Monk P., and Vacus O. Error estimates for a numerical scheme for ferromagnetic problems. SIAM J. Numer. Anal. 36 3 (1998) 696-718
24. Nocheto R.H., Schmidt A., and Verdi C. A posteriori error estimation and adaptivity for degenerate parabolic problems. Math. Comp. 69 229 (2000) 1-24
25. Prohl A. Computational Micromagnetism. Adv. in Numer. Math. vol. XVI (2001), Teubner, Leipzig
26. Slodička M., and Baňas L.'. A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert system. Appl. Math. Comput. 158 1 (2004) 79-99
27. Su F., and Guo B. The global smooth solution for Landau-Lifshitz-Maxwell equation without dissipation. J. Partial Differential Equations 11 3 (1998) 193-208
28. Visintin A. On Landau-Lifshitz' equations for ferromagnetism. Japan J. Appl. Math. 2 (1985) 69-84
29. Weiss P. L'hypothèse du champ moléculaire et la proprièté ferromagnetique. J. Physique 6 (1907) 661-690