full
search.png

Search

close.png

Cancel

arrow
Volume 38, Issue 4
Unfitted Spectral Element Method for Interfacial Models

Nicolas Gonzalez, Hailong Guo & Xu Yang

DOI: 10.4208/cicp.OA-2024-0056

Commun. Comput. Phys., 38 (2025), pp. 987-1016.

Published online: 2025-09

Preview Purchase PDF 97 708

Cited by

google scholar semantic scholar
Export citation
  • Abstract

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.

  • Keywords

Elliptic interface problem, interface eigenvalue problem, unfitted Nitsche’s method, $hp$ estimate, ghost penalty.

  • AMS Subject Headings

65N30, 65N25, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-38-987, author = {Gonzalez , NicolasGuo , Hailong and Yang , Xu}, title = {Unfitted Spectral Element Method for Interfacial Models}, journal = {Communications in Computational Physics}, year = {2025}, volume = {38}, number = {4}, pages = {987--1016}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0056}, url = {http://global-sci.org/intro/article_detail/cicp/24351.html} }
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 -

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.

Gonzalez , NicolasGuo , Hailong and Yang , Xu. (2025). Unfitted Spectral Element Method for Interfacial Models. Communications in Computational Physics. 38 (4). 987-1016. doi:10.4208/cicp.OA-2024-0056
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard