Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media

  • Authors:

  • Bo Wang;Ziqing Xie;Zhimin Zhang

  • Affiliations:

  • College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University, Changsha, ...;College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University, Changsha, ...;College of Mathematics and Computational Science, Sun-Yat-sen University, Guangzhou, Guangdong 510275, China and Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

A discontinuous Galerkin method for the numerical approximation of time-dependent Maxwell equations in three different dispersive media is introduced. Both the L^2-stability and error estimate of the DG method are discussed in detail. We show that the proposed method has an accuracy of O(h^k^+^1^2) under the L^2-norm when polynomials of degree k in space are used. Furthermore, numerical experiments are provided to justify our theoretical analysis.