A high order unfitted finite element method for time-Harmonic Maxwell interface problems

In this paper, we propose a high order unfitted finite element method for solving time-harmonic 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.