Numerical analysis of an explicit approximation scheme for the Landau-lifshitz-gilbert equation

Mathematics of Computation

Volumn 77, Issue 262, 2008, Pages 773-788

  Bartels, Sören ^a,b   Ko, Joy ^c   Prohl, Andreas ^d  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF BONN   (Germany)

^c BROWN UNIVERSITY   (United States)

^d UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42349111133     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-02079-0     Document Type: Article

References (16)

1. François Alouges and Pascal Jaisson. Convergence of a finite element discretization for the Landau-Lifshitz equations in micromagnetism. Math. Models Methods Appl. Sci., 16(2):299-316, 2006. MR2210092 (2007b:65091)
2. François Alouges and Alain Soyeur. On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness. Nonlinear Anal., 18(11):1071-1084, 1992. MR1167422 (93i:35148)
3. John W. Barrett, Sören Bartels, Xiaobing Feng, and Andreas Prohl. A convergent and constraint-preserving finite finite element method for the p-harmonic flow into spheres. SIAM J. Numer. Anal. (accepted), 2006.
4. Kung-Ching Chang, Wei Yue Ding, and Rugang Ye. Finite-time blowup of the heat flow of harmonic maps from surfaces. J. Differential Geom., 36(2):507-515, 1992. MR1180392 (93h:58043)
5. Jean-Michel Coron. Nonuniqueness for the heat flow of harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire, 7(4):335-344, 1990. MR1067779 (91g:58058)
6. Weinan E and Xiao-Ping Wang. Numerical methods for the Landau-Lifshitz equation. SIAM J. Numer. Anal., 38(5):1647-1665 (electronic), 2000. MR1813249 (2002g:65112)
7. Josef Fidler and Thomas Schrefl. Micromagnetic modelling - the current state of the art. 33:R135-R156, 2000.
8. Boling Guo and Min-Chun Hong. The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps. Calc. Var. Partial Differential Equations, 1(1):311-334, 1993. MR1261548 (94m:58059)
9. Stephen Gustafson, Kyungkeun Kang, and Tai-Peng Tsai. Schrödinger flow near harmonic maps. Comm. Pure Appl. Math., 60(4):463-499, 2007. MR2290708
10. 2. Nonlinearity, 18(6):2681-2714, 2005. MR2176953 (2006h:35260)
11. Martin Kruzik and Andreas Prohl. Recent developments in the modeling, analysis, and numerics of ferromagnetism. SIAM Review, 48(3):439-483, 2006. MR2278438
12. Christof Melcher. Logarithmic lower bounds for Néel walls. Calc. Var. Partial Differential Equations, 21(2):209-219, 2004. MR2085302 (2005m:49075)
13. Francesca Pistella and Vanda Valente. Numerical study of the appearance of singularities in ferromagnets. Adv. Math. Sci. Appl., 12(2):803-816, 2002. MR1943993 (2003m:82101)
14. Jalal Shatah and Chongchun Zeng. Schrödinger maps and anti-ferromagnetic chains. Comm. Math. Phys., 262(2):299-315, 2006. MR2200262 (2006m:58043)
15. Michael Struwe. On the evolution of harmonic mappings of Riemannian surfaces. Comment. Math. Helv., 60(4):558-581, 1985. MR826871 (87e:58056)
16. Xiao-Ping Wang, Carlos J. García-Cervera, and Weinan E. A Gauss-Seidel projection method for micromagnetics simulations. J. Comput. Phys., 171(1):357-372, 2001. MR1843650 (2002f:78015)