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


UNIFIED ANALYSIS OF TIME DOMAIN MIXED FINITE ELEMENT METHODS FOR MAXWELL'S EQUATIONS IN DISPERSIVE MEDIA

Jichun Li 1, Zhimin Zhang 2

1 Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA
2 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

Received 2009-3-16 Accepted 2009-9-15
Available online 2010-5-1
doi:10.4208/jcm.1001-m3072

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-N\'ed\'elec spaces. Extensions to multiple pole dispersive media are presented also.

Key words: Maxwell's equations, Dispersive media,

AMS subject classifications: 65N30, 35L15, 78-08


Email: jichun@unlv.nevada.edu, zzhang@math.wayne.edu
 

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