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

TL;DR

This paper introduces a high-order unfitted finite element method for solving time-harmonic Maxwell interface problems, demonstrating stability, error estimates, and effective numerical performance on complex 3D domains.

Contribution

It develops a novel high-order unfitted finite element approach within a discontinuous Galerkin framework for Maxwell interface problems, including stability and error analysis.

Findings

Proves $H^2$ regularity for Maxwell interface solutions with $C^2$ interfaces.

Establishes stability and hp a priori error estimates.

Numerical results confirm the method's effectiveness on 3D curved domains.

Abstract

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.