TY - JOUR
T1 - A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems
AU - Chen , Zhiming
AU - Li , Ke
AU - Lyu , Maohui
AU - Xiang , Xueshaung
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 822
EP - 849
PY - 2024
DA - 2024/10
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1033
UR - https://global-sci.org/intro/article_detail/ijnam/23462.html
KW - Maxwell interface problem, high order unfitted finite element method, $hp$ a priori error estimate.
AB - <p style="text-align: justify;">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.</p>