论文标题
Navier-Lamé特征值问题的有限元分析
Finite element analysis for the Navier-Lamé eigenvalue problem
论文作者
论文摘要
本文考虑了所谓的Navier-Lamé系统，本文介绍了弹性方程的特征值问题的分析。这样的系统引入了一些线性和弹性结构的位移，旋转和压力。光谱问题的分析基于紧凑的操作者理论。为了近似系统的特征频率和本征函数，考虑了基于$ k \ geq 1 $的多项式中的有限元方法。提出了收敛和误差估计。进行后验错误分析，其中证明了所提出的估计器的可靠性和效率。我们结束了报告一系列数值测试的贡献，以评估先验和后验估计的拟议数值方法的性能。
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 $k\geq 1$ 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.
