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arXiv · 2209.11825

Finite element analysis for the Navier-Lam\'e eigenvalue problem

Felipe Lepe·Gonzalo Rivera·Jesus Vellojin
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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 $k\geq 1$ 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.

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Felipe Lepe, Gonzalo Rivera, Jesus Vellojin. 2022-09-23. Finite element analysis for the Navier-Lam\'e eigenvalue problem. https://arxiv.org/abs/2209.11825

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