Study On The Finite Element Algorithms Of Landau-lifshitz Equation

Landau-lifshitz(LL)equation is an important mathematical model in solving ferromagnetic problems.This equation simulates the magnetization motion of ferromagnetic medium under different conditions,and describes the magnetization evolution of continuous ferromagnets,and is widely used in micromagnetism and other fields.In this thesis,the first-order backward Euler projection finite element algorithm and the linearized second-order BDF scheme are studied for the LL equation without external magnetic field.For the first-order projection algorithm,the temporal-spatial error estimation of O(?2+h2)is obtained under the time step condition ?=O(h2).For the second-order BDF scheme,we obtain the second-order convergence rate of O(?2+h2).In addition,numerical experiments are given to support our theoretical analysis.