Space-time discontinuous galerkin method for maxwell equations in dispersive media |
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| Authors: | Bo WANG Ziqing XIE Zhimin ZHANG |
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| Institution: | 1. 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;2. Beijing Computational Science Research Center, Beijing 100084, China;3. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA |
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| Abstract: | In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in 29] is applied to solve the underlying problem. Unconditional L2-stability and error estimate of order O(τr+1+hk+1/2) are obtained when polynomials of degree at most r and k are used for the temporal discretization 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. |
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| Keywords: | Maxwell equations dispersive media space-time DG method L2-stability L2-error estimate |
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