Finite element analysis for the Navier-Lam\'e eigenvalue problem
Abstract
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and elastic structure. The analysis of the spectral problem is based in the compact operators theory. A finite element method based in polynomials of degree are considered in order to approximate the eigenfrequencies and eigenfunctions of the system. Convergence and error estimate are presented. An a posteriori error analysis is performed, where the reliability and efficiency of the proposed estimator is proved. We end this contribution reporting a series of numerical tests in order to assess the performance of the proposed numerical method, for the a priori and a posteriori estimates.
Cite
@article{arxiv.2209.11825,
title = {Finite element analysis for the Navier-Lam\'e eigenvalue problem},
author = {Felipe Lepe and Gonzalo Rivera and Jesus Vellojin},
journal= {arXiv preprint arXiv:2209.11825},
year = {2022}
}