求解二维时谐Maxwell方程的一种混合有限元新格式

doi:10.12286/jssx.2016.4.429

计算数学 ›› 2016, Vol. 38 ›› Issue (4): 429-441.DOI: 10.12286/jssx.2016.4.429

求解二维时谐Maxwell方程的一种混合有限元新格式

曹济伟^1,2

1. 河南财经政法大学数学与信息科学学院, 郑州 450000;
2. 南开大学数学科学学院, 天津 300071

收稿日期:2016-01-22 出版日期:2016-12-15 发布日期:2016-10-13
基金资助:
国家自然科学基金11071132，11171168，91430106，11571266资助.

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曹济伟. 求解二维时谐Maxwell方程的一种混合有限元新格式[J]. 计算数学, 2016, 38(4): 429-441.

Cao Jiwei. A NEW MIXED FINITE ELEMENT SCHEME FOR SOLVING 2D TIME-HARMONIC MAXWELL-TYPE PROBLEM[J]. Mathematica Numerica Sinica, 2016, 38(4): 429-441.

A NEW MIXED FINITE ELEMENT SCHEME FOR SOLVING 2D TIME-HARMONIC MAXWELL-TYPE PROBLEM

Cao Jiwei^1,2

1. School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450000, China;
2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Received:2016-01-22 Online:2016-12-15 Published:2016-10-13

本文，我们提出一种新的求解二维时谐Maxwell方程的H¹-协调节点连续混合有限元格式.由于加上若干稳定化项和投影项，得到的混合变分形式是稳定的.我们证明了双线性形式满足连续性，K^h-强制性和Inf-Sup条件，因此，解是存在唯一的.此外，我们也给出了拟优的误差估计和相应的收敛阶.

关键词： 混合有限元方法, Maxwell方程, 投影方法, 拟优误差估计

In this paper, we propose a new H¹-conforming nodal-continuous mixed finite element scheme. Several stabilizations and projections are added into the mixed finite element scheme and thus the stability of the variational system is achieved. We prove that the bilinear forms satisfy continuity, K^h-coercivity and Inf-Sup condition, and hence the existence and uniqueness of solution hold. Furthermore, quasi-optimal error estimates and convergence rate are derived.

Key words: Mixed finite element method, Maxwell equations, Projection method, Quasioptimal error estimate

MR(2010)主题分类:

65N15
65N30

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求解二维时谐Maxwell方程的一种混合有限元新格式

A NEW MIXED FINITE ELEMENT SCHEME FOR SOLVING 2D TIME-HARMONIC MAXWELL-TYPE PROBLEM

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