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Volume 28, Issue 5
Unified Analysis of Time Domain Mixed Finite Element Methods for Maxwell's Equations in Dispersive Media

Jichun Li & Zhimin Zhang

DOI: 10.4208/jcm.1001-m3072

J. Comp. Math., 28 (2010), pp. 693-710.

Published online: 2010-10

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  • Abstract

In this paper, we consider the time dependent Maxwell's equations when dispersive media are involved. The Crank-Nicolson mixed finite element methods are developed for three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for all three models solved by the Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also.

  • Keywords

Maxwell's equations, Dispersive media, Mixed finite element method.

  • AMS Subject Headings

65N30, 35L15, 78-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-693, author = {Jichun Li and Zhimin Zhang}, title = {Unified Analysis of Time Domain Mixed Finite Element Methods for Maxwell's Equations in Dispersive Media}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {5}, pages = {693--710}, abstract = {

In this paper, we consider the time dependent Maxwell's equations when dispersive media are involved. The Crank-Nicolson mixed finite element methods are developed for three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for all three models solved by the Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1001-m3072}, url = {http://global-sci.org/intro/article_detail/jcm/8544.html} }
TY - JOUR T1 - Unified Analysis of Time Domain Mixed Finite Element Methods for Maxwell's Equations in Dispersive Media AU - Jichun Li & Zhimin Zhang JO - Journal of Computational Mathematics VL - 5 SP - 693 EP - 710 PY - 2010 DA - 2010/10 SN - 28 DO - http://doi.org/10.4208/jcm.1001-m3072 UR - https://global-sci.org/intro/article_detail/jcm/8544.html KW - Maxwell's equations, Dispersive media, Mixed finite element method. AB -

In this paper, we consider the time dependent Maxwell's equations when dispersive media are involved. The Crank-Nicolson mixed finite element methods are developed for three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for all three models solved by the Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also.

Jichun Li and Zhimin Zhang. (2010). Unified Analysis of Time Domain Mixed Finite Element Methods for Maxwell's Equations in Dispersive Media. Journal of Computational Mathematics. 28 (5). 693-710. doi:10.4208/jcm.1001-m3072
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