TY - JOUR
T1 - Unfitted Spectral Element Method for Interfacial Models
AU - Gonzalez , Nicolas
AU - Guo , Hailong
AU - Yang , Xu
JO - Communications in Computational Physics
VL - 4
SP - 987
EP - 1016
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0056
UR - https://global-sci.org/intro/article_detail/cicp/24351.html
KW - Elliptic interface problem, interface eigenvalue problem, unfitted Nitsche’s method, $hp$ estimate, ghost penalty.
AB - <p style="text-align: justify;">In this paper, we propose an unfitted spectral element method for solving
elliptic interface and corresponding eigenvalue problems. The novelty of the proposed
method lies in its combination of the spectral accuracy of the spectral element method
and the flexibility of the unfitted Nitsche’s method. We also use tailored ghost penalty
terms 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.</p>