Volume 14, Issue 4
Space-time Discontinuous Galerkin Method for Maxwell's Equations

Ziqing Xie, Bo Wang & Zhimin Zhang

Commun. Comput. Phys., 14 (2013), pp. 916-939.

Published online: 2013-10

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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 Galerkinmethods areused todiscretizenot only the spatial domain butalso the temporaldomain. The proposednumerical scheme is provedtobe unconditionally stable, and a convergent rate O((△t)r+1 +hk+1/2) is established under the L2-normwhen polynomials of degreeat most r and k areused 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 (△t)2r+1 in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points.


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@Article{CiCP-14-916, author = {Ziqing Xie, Bo Wang and Zhimin Zhang}, title = {Space-time Discontinuous Galerkin Method for Maxwell's Equations}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {4}, pages = {916--939}, 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 Galerkinmethods areused todiscretizenot only the spatial domain butalso the temporaldomain. The proposednumerical scheme is provedtobe unconditionally stable, and a convergent rate O((△t)r+1 +hk+1/2) is established under the L2-normwhen polynomials of degreeat most r and k areused 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 (△t)2r+1 in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.230412.271212a}, url = {http://global-sci.org/intro/article_detail/cicp/7186.html} }
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