Immersed Finite Element Method for Eigenvalue Problems in Elasticity
Seung-Woo Lee, Do Young Kwak, Imbo Sim · Advances in Applied Mathematics and Mechanics · 2018
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 adopting spectral analysis methods for the classical eigenvalue problem. Numerical experiments demonstrate our theoretical results.