@Article{CiCP-11-1673,
author = {Liping Gao and Dong Liang},
title = {New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {5},
pages = {1673--1696},
abstract = {<p style="text-align: justify;">The symmetric energy-conserved splitting FDTD scheme developed in [1] is
a very new and efficient scheme for computing the Maxwell&#39;s equations. It is based on
splitting the whole Maxwell&#39;s equations and matching the <em>x</em>-direction and <em>y</em>-direction
electric fields associated to the magnetic field symmetrically. In this paper, we make
further study on the scheme for the 2D Maxwell&#39;s equations with the PEC boundary
condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme
in the discrete H<sup>1</sup>-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H<sup>1</sup>-norm. By the new energy-conserved identities, the
super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is
of second order convergence in both time and space steps in the discrete H<sup>1</sup>-norm.
Numerical experiments are carried out and confirm our theoretical results.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.121110.030611a},
url = {http://global-sci.org/intro/article_detail/cicp/7429.html}
}