Immersed Finite Element Method for Eigenvalue Problem
Provides theoretical guarantees for IFEM in eigenvalue problems, which is incremental for numerical analysis researchers.
The paper proves stability and optimal convergence of an immersed finite element method for elliptic eigenvalue problems with immersed interfaces, using Crouzeix-Raviart nonconforming elements, with numerical validation.
We consider the approximation of elliptic eigenvalue problem with an immersed interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix-Raviart $P_1$-nonconforming approximation. We show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem. We analyze the IFEM for elliptic eigenvalue problem with an immersed interface and derive the optimal convergence of eigenvalues. Numerical experiments demonstrate our theoretical results.