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| 求解二维时谐Maxwell方程的一种混合有限元新格式 | |
| 引用本文： | 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. |
| 作者姓名： | 曹济伟 |
| 作者单位： | 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 |
| 基金项目： | 国家自然科学基金11071132;11571266资助. |
| 摘 要： | 本文,我们提出一种新的求解二维时谐Maxwell方程的H~1-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 |
| 收稿时间： | 2016-01-22; |
A NEW MIXED FINITE ELEMENT SCHEME FOR SOLVING 2D TIME-HARMONIC MAXWELL-TYPE PROBLEM |
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| 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. | |
| Authors: | Cao Jiwei |
| Institution: | 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 |
| Abstract: | 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, Kh-coercivity and Inf-Sup condition, and hence the existence and uniqueness of solution hold. Furthermore, quasi-optimal error estimates and convergence rate are derived. |
| Keywords: | Mixed finite element method Maxwell equations Projection method Quasi-optimal error estimate |
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