@Article{CiCP-14-4,
author = {},
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 = {<p style="text-align: justify;">A fully discrete discontinuous Galerkin method is introduced for solving
time-dependent Maxwell&#39;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 $\mathcal{O}((∆t)^{r+1}+h^{k+1/2})$ is established under the $L^2$ -norm when polynomials of degree at most $r$ 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 $(∆t)^{2r+1}$ in
time step is observed numerically for the numerical fluxes w.r.t. temporal variable at
the grid points.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230412.271212a},
url = {https://global-sci.com/article/80583/space-time-discontinuous-galerkin-method-for-maxwells-equations}
}