Please use this identifier to cite or link to this item: https://doi.org/10.4208/cicp.230412.271212a
Title: Space-time discontinuous Galerkin method for Maxwell's equations
Authors: Xie, Z.
Wang, B. 
Zhang, Z.
Keywords: Discontinuous Galerkin method
Full-discretization
L2-error estimate
L2-stability
Maxwell's equations
Ultra-convergence
Issue Date: Oct-2013
Source: Xie, Z., Wang, B., Zhang, Z. (2013-10). Space-time discontinuous Galerkin method for Maxwell's equations. Communications in Computational Physics 14 (4) : 916-939. ScholarBank@NUS Repository. https://doi.org/10.4208/cicp.230412.271212a
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 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 script O sign((Δt)r+1 + hk+1/2) is established under the L2-normwhen 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 (Δt)2r+1 in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points. © 2013 Global-Science Press.
Source Title: Communications in Computational Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/133099
ISSN: 18152406
DOI: 10.4208/cicp.230412.271212a
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