Acta mathematica scientia, Series B >
SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA
Received date: 2013-10-28
Revised date: 2014-01-10
Online 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.
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 + hk+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.
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 . DOI: 10.1016/S0252-9602(14)60089-8
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