Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6033
Title: Developing finite element methods for maxwell's equations in a cole-cole dispersive medium
Authors: Li, J
Huang, Y
Lin, Y 
Keywords: Maxwell's equations
Dispersive medium
Cole–Cole model
Finite element method
Issue Date: 2011
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on scientific computing, v. 33, no. 6, p. 3153–3174 How to cite?
Journal: SIAM journal on scientific computing 
Abstract: In this paper, we consider the time-dependent Maxwell's equations when Cole–Cole dispersive medium is involved. The Cole–Cole model contains a fractional time derivative term, which couples with the standard Maxwell's equations in free space and creates some challenges in developing and analyzing time-domain finite element methods for solving this model as mentioned in our earlier work [J. Li, J. Sci. Comput., 47 (2001), pp. 1–26]. By adopting some techniques developed for the fractional diffusion equations [V.J. Ervin, N. Heuer, and J.P. Roop, SIAM J. Numer. Anal., 45 (2007), pp. 572–591], [Y. Lin and C. Xu, J. Comput. Phys., 225 (2007), pp. 1533–1552], [F. Liu, P. Zhuang, V. Anh, I. Turner, and K. Burrage, Appl. Math. Comput., 191 (2007), pp. 12–20], we propose two fully discrete mixed finite element schemes for the Cole–Cole model. Numerical stability and optimal error estimates are proved for both schemes. The proposed algorithms are implemented and detailed numerical results are provided to justify our theoretical analysis.
URI: http://hdl.handle.net/10397/6033
ISSN: 1064-8275
EISSN: 1095-7197
DOI: 10.1137/110827624
Rights: © 2011 Society for Industrial and Applied Mathematics
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