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 -

An implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell's equations in metamaterials. The Maxwell'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.