Convergence Of An Implicit Finite Element Method For The LLG Equation With External Magnetic Field

In1953, Laudau and Lifshitz proposed the famous magnetization movement equationwhen they studied dispersion theory of ferromagnet permeability. Because the magnetic is thebasic property of substance,and is the essential of the materials science, it is very important touse the methods of mathematical physics to study the magnetic of substance.In this thesis, numerical simulation of the LLG equations with external magnetic fieldsis researched and we propose an implicit scheme to approach the weak solution of the LLGequations with external magnetic fields.The first part of thesis is introduction, in this part we describe the theoretical backgroundand a state of the art of LLG equation. In the end of this part we introduce the main contents ofthis thesis.The second part of thesis is the preliminaries of finite element and the theoretical back-ground of the whole thesis.The third part of thesis is devoted to propose an implicit scheme and the weak solution ofthe LLG equations with external magnetic field is defined. we prove the sequence produced byalgorithm converges to weak solution.In the fourth part of thesis, the nonlinear system of the implicit algorithm is solved by thealgorithm of fixed-point iteration, and the convergence of the fixed-point iteration algorithm isproved.The fifth part of thesis is error analysis.