• 论文 •

### 一类带有铁磁材料参数的非线性涡流问题的A-φ有限元法

1. 1. 河南理工大学数学与信息科学学院, 河南焦作 454000;
2. 中国传媒大学理工学部, 北京 100024;
3. 中国传媒大学理工学部, 北京 100024
• 收稿日期:2015-04-15 出版日期:2016-04-15 发布日期:2016-05-13
• 通讯作者: 康彤,E-mail:kangtong@cuc.edu.cn.
• 基金资助:

国家自然科学基金(批准号11571352)资助.

Wang Yanfang, Wang Ran, Kang Tong. A-φ FINITE ELEMENT METHOD FOR A NONLINEAR EDDY CURRENT PROBLEM WITH FERROMAGNETIC MATERIALS[J]. Mathematica Numerica Sinica, 2016, 38(2): 125-142.

### A-φ FINITE ELEMENT METHOD FOR A NONLINEAR EDDY CURRENT PROBLEM WITH FERROMAGNETIC MATERIALS

Wang Yanfang1,2, Wang Ran3, Kang Tong3

1. 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan, China;
2. College of Sciences and Engineering, School of Sciences, Communication University of China, Beijing 100024, China;
3. College of Sciences and Engineering, School of Sciences, Communication University of China, Beijing 100024, China
• Received:2015-04-15 Online:2016-04-15 Published:2016-05-13

In this paper we study a fully discrete A-φ finite element scheme to solve a class of nonlinear eddy current equations with ferromagnetic materials by backward Euler discretization in time and nodal finite elements in space. The nonlinearity is reflected in the relationship between the magnetic field and the magnetic flux density. We first present a nonlinear time discretization scheme for approximation in suitable function spaces. The well-posedness of the approximate problem is established by examining its weak formulation. The convergence of the approximate solution to the weak solution is proved. Next, we design full discretization scheme and discuss its error estimate. Finally, we perform two numerical experiments to verify the theoretical result.

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