Unfitted Spectral Element Method for interfacial models

TL;DR

This paper introduces an unfitted spectral element method that combines spectral accuracy with flexibility for solving elliptic interface and eigenvalue problems, achieving optimal convergence and spectral accuracy.

Contribution

The paper presents a novel unfitted spectral element method that integrates spectral accuracy with Nitsche's method and ghost penalties for elliptic interface problems.

Findings

Achieves optimal $hp$ convergence rates.

Demonstrates spectral accuracy in polynomial degree.

Enhances robustness with ghost penalty terms.

Abstract

In this paper, we propose the 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.