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

doi:10.12286/jssx.2016.2.125

计算数学 ›› 2016, Vol. 38 ›› Issue (2): 125-142.DOI: 10.12286/jssx.2016.2.125

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

王艳芳^1,2, 王然³, 康彤³

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.

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王艳芳, 王然, 康彤. 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[J]. 计算数学, 2016, 38(2): 125-142.

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 Yanfang^1,2, Wang Ran³, Kang Tong³

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

针对带有铁磁材料的非线性涡流问题,其非线性性通常体现在磁场强度和磁感应强度的关系上.本文提出了一种全离散的有限元A-φ格式,分别在时间和空间上采用向后欧拉公式以及节点有限元进行离散.首先,在合适的函数空间里给出时间上的半离散格式,通过考察其弱形式建立相应的适定性理论,并证明近似解收敛于弱解.其次,给出全离散格式并讨论其误差估计.最后,给出两个数值算例以验证理论结果.

关键词： 非线性涡流问题, A-&phi, 有限元法, 适定性, 误差估计

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.

Key words: Nonlinear eddy current problem, A-φ finite element method, Well-posedness, Error estimate

MR(2010)主题分类:

65N15
65C30

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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

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

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