Unfitted Spectral Element Method for Interfacial Models (Communications in Computational Physics, 2025)
In this paper, we propose an unfitted spectral element method for solvingelliptic interface and corresponding eigenvalue problems. The novelty of the proposedmethod lies in its combination of the spectral accuracy of the spectral element methodand the flexibility of the unfitted Nitsche’s method. We also use tailored ghost penaltyterms to enhance its robustness. We establish optimal $hp$ convergence rates for both elliptic interface problems and interface eigenvalue problems. Additionally, we demonstrate spectral accuracy for model problems in terms of polynomial degree.
Keywords: Elliptic interface problem; interface eigenvalue problem; unfitted Nitsche’s method; $hp$ estimate; ghost penalty