SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

doi:10.1016/S0252-9602(14)60089-8

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1357-1376.doi: 10.1016/S0252-9602(14)60089-8

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SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

汪波|谢资清|张智民

College of Mathematics and Computer Science, and Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha 410081, China； Beijing Computational Science Research Center, Beijing 100084, China, and Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

收稿日期:2013-10-28 修回日期:2014-01-10 出版日期:2014-09-20 发布日期:2014-09-20
基金资助:
The first author is supported by NSFC (11341002). The second author is supported by NSFC (11171104, 10871066) and the Construct Program of the Key Discipline in Hunan. The third author is supported in part by US National Science Foundation under Grant DMS-1115530.

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

WANG Bo, XIE Zi-Qing, ZHANG Zhi-Min

College of Mathematics and Computer Science, and Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha 410081, China； Beijing Computational Science Research Center, Beijing 100084, China, and Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

Received:2013-10-28 Revised:2014-01-10 Online:2014-09-20 Published:2014-09-20
Supported by:
The first author is supported by NSFC (11341002). The second author is supported by NSFC (11171104, 10871066) and the Construct Program of the Key Discipline in Hunan. The third author is supported in part by US National Science Foundation under Grant DMS-1115530.

摘要/Abstract

摘要：

In this paper, a unified model for time-dependentMaxwell equations in dispersive media is considered. The space-time DG method developed in^[29] is applied to solve the un-derlying problem. Unconditional L²-stability and error estimate of order O(τ ^r⁺¹ + h^k^+1/2) are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r + 1 in temporal variable t.

关键词: Maxwell equations, dispersive media, space-time DG method, L²-stability, L²-error estimate

Abstract:

Key words: Maxwell equations, dispersive media, space-time DG method, L²-stability, L²-error estimate

中图分类号:

65N30

汪波, 谢资清, 张智民. SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA[J]. 数学物理学报(英文版), 2014, 34(5): 1357-1376.

WANG Bo, XIE Zi-Qing, ZHANG Zhi-Min. SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA[J]. Acta mathematica scientia,Series B, 2014, 34(5): 1357-1376.

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SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

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