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

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.