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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 regularity of the
solution to Maxwell interface problems with 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