Finite element analysis for the Navier-Lamé eigenvalue problem
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The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lamé 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≥ 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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