A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems

Abstract

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.