TY - JOUR
T1 - Implicit DG Method for Time Domain Maxwell's Equations Involving Metamaterials
AU - Wang , Jiangxing
AU - Xie , Ziqing
AU - Chen , Chuanmiao
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 796
EP - 817
PY - 2018
DA - 2018/05
SN - 7
DO - http://doi.org/10.4208/aamm.2014.m725
UR - https://global-sci.org/intro/article_detail/aamm/12240.html
KW - 
AB - <p style="text-align: justify;">An implicit discontinuous Galerkin method is introduced to solve the time-domain
Maxwell&#39;s equations in metamaterials. The Maxwell&#39;s equations in metamaterials
are represented by integral-differential equations. Our scheme is based on discontinuous
Galerkin method in spatial domain and Crank-Nicolson method in temporal
domain. The fully discrete numerical scheme is proved to be unconditionally stable.
When polynomial of degree at most $p$ is used for spatial approximation, our scheme is
verified to converge at a rate of $\mathcal{O}(τ^2+h^{p+1/2})$. Numerical results in both 2D and 3D
are provided to validate our theoretical prediction.</p>