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Space-Time Discontinuous Galerkin Method for Maxwell’s Equations

Published online by Cambridge University Press:  03 June 2015

Ziqing Xie ,
Bo Wang  and
Zhimin Zhang
Ziqing Xie*
Affiliation:
School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University, Changsha, Hunan 410081, China
Bo Wang*
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore
Zhimin Zhang*
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, 510275, China
*
Email:ziqingxie@yahoo.com.cn
Corresponding author.Email:bowanghn@gmail.com
Email:ag7761@wayne.edu
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Abstract

A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations. Distinguished from the Runge-Kutta discontinuous Galerkin method (RKDG) and the finite element time domain method (FETD), in our scheme, discontinuous Galerkin methods are used to discretize not only the spatial domain but also the temporal domain. The proposed numerical scheme is proved to be unconditionally stable, and a convergent rate is established under the L2-norm when polynomials of degree atmost r and k are used for temporal and spatial approximation, respectively. Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction. An ultra-convergence of order in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points.

Keywords

35Q6165M1265M6065N12Discontinuous Galerkin methodMaxwell’s equationsfull-discretization L2-error estimateL2-stabilityultra-convergence
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 916 - 939
Copyright
Copyright © Global Science Press Limited 2013

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