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Superconvergence analysis for Maxwell's equations in dispersive media

Authors: Qun Lin and Jichun Li
Journal: Math. Comp. 77 (2008), 757-771
MSC (2000): Primary 65N30, 35L15, 78Mxx
Published electronically: November 13, 2007
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Abstract: In this paper, we consider the time dependent Maxwell's equations in dispersive media on a bounded three-dimensional domain. Global superconvergence is obtained for semi-discrete mixed finite element methods for three most popular dispersive media models: the isotropic cold plasma, the one-pole Debye medium, and the two-pole Lorentz medium. Global superconvergence for a standard finite element method is also presented. To our best knowledge, this is the first superconvergence analysis obtained for Maxwell's equations when dispersive media are involved.

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Additional Information

Qun Lin
Affiliation: LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

Jichun Li
Affiliation: Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 Maryland Parkway, Box 454020, Las Vegas, Nevada 89154-4020

Keywords: Maxwell's equations, dispersive media, superconvergence analysis
Received by editor(s): May 25, 2006
Received by editor(s) in revised form: January 26, 2007
Published electronically: November 13, 2007
Article copyright: © Copyright 2007 American Mathematical Society