Convergence of a finite element discretization for the Landau-Lifshitz equations in micromagnetism

被引：89
作者：
Alouges, F
Jaisson, P
机构：
[1] Univ Orsay, Math Lab, F-91405 Orsay, France
[2] Ecole Normale Super, Ctr Math & Leurs Applicat, F-94235 Cachan, France
[3] Ecole Cent Paris, Lab MAS, F-92295 Chatenay Malabry, France
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2006年 / 16卷 / 02期
关键词：
Finite elements; micromagnetism; Landau-Lifshitz equations; weak solutions;
D O I：
10.1142/S0218202506001169
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we propose a new space and time finite elements discretization of the Landau-Lifshitz equations which may be readily used for numerical computations. We then prove its convergence to a weak solution in the sense given by Alouges and Soyeur or Labbe in the literature.
引用
收藏
页码：299 / 316
页数：18
相关论文
共 14 条
[1]   ON GLOBAL WEAK SOLUTIONS FOR LANDAU-LIFSHITZ EQUATIONS - EXISTENCE AND NONUNIQUENESS [J].
ALOUGES, F ;
SOYEUR, A .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 18 (11) :1071-1084
[2]   Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method [J].
Alouges, FC .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2001, 6 (27) :629-647
[3]  
BETHUEL F, 1990, NONLINEAR DIFFUSION
[4]  
Braess D., 1997, FINITE ELEMENTE
[5]  
Brown W.F., 1963, MICROMAGNETICS INTER
[6]  
Carbou G., 2001, Commun. Appl. Anal, V5, P17
[7]  
Carbou G., 2001, Diff. Integral Equ, V14, P213
[8]   THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN AND HARMONIC MAPS [J].
GUO, BL ;
HONG, MC .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1993, 1 (03) :311-334
[9]   Finite element calculations on the single-domain limit of a ferromagnetic cube -: a solution to μMAG Standard Problem No. 3 [J].
Hertel, R ;
Kronmüller, H .
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS, 2002, 238 (2-3) :185-199
[10]  
LABBE S, 1998, THESIS U PARIS 13
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