Maxwell-Landau-Lifshitz方程的一阶半隐欧拉方法的时间收敛性

Temporal Convergence of the First-order Semi-implicit Euler Scheme for the Maxwell-Landau-Lifshitz Equations

研究了求解Maxwell-Landau-Lifshitz方程的一阶Euler时间离散算法,使得数值解可近似满足单位长度的非凸约束.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H1-范数和H(curl)-范数下的最优误差估计.

This paper studies the first-order Euler time discrete algorithm for solving the Maxwell-LandauLifshitz equations,which makes the numerical solution satisfy the nonconvex constraint of unit length point by point.By means of mathematical induction,the optimal error estimates of exact solution and numerical solution about magnetization and magnetic field under H1-norm and H(curl)-norm are obtained respectively.