@Article{NMTMA-13-788,
author = {Gao , LipingSang , Xiaorui and Shi , Rengang},
title = {Energy Identities and Stability Analysis of the Yee Scheme for 3D Maxwell Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {3},
pages = {788--813},
abstract = {<p style="text-align: justify;">In this paper numerical energy identities of the Yee scheme on uniform grids for&nbsp; three dimensional Maxwell equations with periodic boundary conditions&nbsp; are proposed and expressed in terms of the $L^2$, $H^1$ and $H^2$ norms. The relations between the $H^1$ or $H^2$ semi-norms and the magnitudes of the curls or the second curls of the fields in the Yee scheme are derived. By the $L^2$ form of the identity it is shown that the solution fields of the Yee scheme is approximately energy conserved. By the $H^1$ or $H^2$ semi norm of the identities, it is proved that the curls or the second curls of the solution of the Yee scheme are approximately magnitude (or energy)-conserved. From these numerical energy identities, the Courant-Friedrichs-Lewy (CFL) stability condition is re-derived, and the stability of the Yee scheme in the $L^2$,&nbsp; $H^1$&nbsp; and $H^2$ norms is then proved. Numerical experiments to compute the numerical energies and convergence orders in the&nbsp; $L^2$, $H^1$ and $H^2$ norms are carried out and the computational results confirm the analysis of the Yee scheme on energy conservation and stability analysis.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0121},
url = {http://global-sci.org/intro/article_detail/nmtma/15785.html}
}