Landau-Lifshitz-Bloch方程的一阶向后欧拉方法的最优误差估计  

Optimal Error Estimates of a First-Order Backward Euler Scheme for the Landau-Lifshitz-Bloch Equation

作　　者：孟裕 MENG Yu(College of Mathematics and Physics,Wenzhou University,Wenzhou,China 325035)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《温州大学学报（自然科学版）》2024年第4期1-10,共10页Journal of Wenzhou University(Natural Science Edition)

摘　　要：研究了求解Landau-Lifshitz-Bloch方程的一阶向后Euler有限元全离散算法.借助数学归纳法,分别得到了精确解和数值解关于磁化强度和磁场在L^(2)和H^(1)范数下的最优误差估计,并通过二维和三维空间的数值结果,验证了所给的理论分析.This paper investigates the first-order backward Euler finite element fully discrete algorithm for solving the Landau-Lifshitz-Bloch(LLB)equation.By using mathematical induction,the optimal error estimates of magnetization and magnetic field under L^(2) and H^(1) norms are obtained for both exact and numerical solutions,respectively.The theoretical analysis is validated by numerical results in 2D and 3D spaces.

关 键 词：Landau-Lifshitz-Bloch方程 最优误差估计 无条件收敛 线性化半隐式格式 有限元法 

分 类 号：O241.82[理学—计算数学]