Volume 9, Issue 2
Nonconforming Mixed Finite Element Method for Time-Dependent Maxwell's Equations with ABC

Changhui Yao & Dongyang Shi

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 193-214.

Published online: 2016-09

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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 semi-discrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

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@Article{NMTMA-9-193, author = {}, title = {Nonconforming Mixed Finite Element Method for Time-Dependent Maxwell's Equations with ABC}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {2}, pages = {193--214}, 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 semi-discrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1427}, url = {http://global-sci.org/intro/article_detail/nmtma/12374.html} }
TY - JOUR T1 - Nonconforming Mixed Finite Element Method for Time-Dependent Maxwell's Equations with ABC JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 193 EP - 214 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1427 UR - https://global-sci.org/intro/article_detail/nmtma/12374.html KW - AB -

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 semi-discrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

Changhui Yao & Dongyang Shi. (2020). Nonconforming Mixed Finite Element Method for Time-Dependent Maxwell's Equations with ABC. Numerical Mathematics: Theory, Methods and Applications. 9 (2). 193-214. doi:10.4208/nmtma.2016.m1427
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