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Int. J. Numer. Anal. Mod., 21 (2024), pp. 822-849.
Published online: 2024-10
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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.
}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1033}, url = {http://global-sci.org/intro/article_detail/ijnam/23462.html} }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.