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Nonconforming Mixed Finite Element Method for Time-dependent Maxwell's Equations with ABC

Published online by Cambridge University Press:  24 May 2016

Changhui Yao  and
Dongyang Shi
Changhui Yao*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China
Dongyang Shi*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China
*
*Corresponding author. Email addresses: chyao@lsec.cc.ac.cn (C. -H. Yao), shi dy@zzu.edu.cn (D. -Y. Shi)
*Corresponding author. Email addresses: chyao@lsec.cc.ac.cn (C. -H. Yao), shi dy@zzu.edu.cn (D. -Y. Shi)
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Abstract

In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semidiscrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

Keywords

65N3065N1535J25Maxwell's equationsAbsorbing boundary conditionNonconforming mixed FEMSemi-discrete and fully discrete schemes
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 2 , May 2016 , pp. 193 - 214
Copyright
Copyright © Global-Science Press 2016 

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