Immersed finite element method for eigenvalue problems in elasticity

TL;DR

This paper develops an immersed finite element method for solving eigenvalue problems in elasticity with interfaces, proving stability and optimal convergence, supported by numerical experiments.

Contribution

It introduces an IFEM based on Crouzeix-Raviart P1-nonconforming elements for interface eigenvalue problems, with theoretical stability and convergence analysis.

Findings

Proves stability and optimal convergence of the proposed method.

Numerical experiments confirm theoretical results.

Abstract

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming element. The stability and the optimal convergence of IFEM for solving eigenvalue problems with interface are proved by adapting spectral analysis methods for the classical eigenvalue problem. Numerical experiments demonstrate our theoretical results.