Immersed finite element method for eigenvalue problems in elasticity
Provides theoretical guarantees for IFEM applied to eigenvalue problems in elasticity with interfaces, which is incremental for the IFEM community.
The paper proves stability and optimal convergence of the immersed finite element method for eigenvalue problems in elasticity with interfaces, supported by numerical experiments.
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.