Nonconforming finite element approximation of time‐dependent Maxwell's equations in Debye medium
Nonconforming finite element approximation of time‐dependent Maxwell's equations in Debye medium
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DOI：
10.1002/num.21843
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发表时间：
2014-09
影响因子：
3.9
通讯作者：
D. Shi;C. Yao
中科院分区：
文献类型：
--
作者：
D. Shi;C. Yao
本文提出了一种新的非协调混合有限元方法，用于逼近三维含德拜介质的麦克斯韦方程。通过使用传统的变分公式，在不增加“稳定性”或“惩罚”项的情况下，我们证明了离散格式是稳健的。借助于单元的典型性质、内插技巧和导数传递技巧，给出了半离散格式和蛙跳全离散格式的收敛分析和误差估计。数值算例表明了该方法的有效性。©2014威利期刊公司Numer方法偏差式30：1654-1673,2014
In this article, a new nonconforming mixed finite element method (FEM) for approximating the Maxwell's equations with Debye medium in three‐dimension are developed. By employing traditional variational formula, without adding “stability” or “penalty” terms, we show that the discrete scheme is robust. With the help of the element's typical properties, interpolation and derivative transfer skills, the convergence analysis is presented and error estimates for semidiscrete and leap‐frog fully‐discrete schemes are obtained, respectively. Numerical example shows the validity of the proposed method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1654–1673, 2014