We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with possible hanging nodes. The $H^2$ regularity of the solution to Maxwell interface problems with $C^2$ interfaces in each subdomain is proved. Practical interface-resolving mesh conditions are introduced under which the hp inverse estimates on three-dimensional curved domains are proved. Stability and hp a priori error estimate of the unfitted finite element method are proved. Numerical results are included to illustrate the performance of the method.

翻译：本文提出了一种求解时谐Maxwell界面问题的高阶非拟合有限元方法。该非拟合有限元方法基于笛卡尔网格（允许存在悬挂节点）上的间断Galerkin框架混合变分形式。我们证明了在子区域具有$C^2$连续界面的Maxwell界面问题解具有$H^2$正则性。通过引入实用的界面解析网格条件，证明了三维曲面域上的hp逆估计。同时证明了该非拟合有限元方法的稳定性与hp先验误差估计。数值实验结果验证了该方法的计算性能。