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

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

Abstract

Abstract:

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.

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

CLC Number:

65N30

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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