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Mathematics > Numerical Analysis

arXiv:2209.11825 (math)
[Submitted on 23 Sep 2022]

Title:Finite element analysis for the Navier-Lamé eigenvalue problem

Authors: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-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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 35Q35, 65N15, 65N25, 65N30, 65N50
Cite as: arXiv:2209.11825 [math.NA]
  (or arXiv:2209.11825v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2209.11825

Submission history

From: Jesus Vellojin [view email]
[v1] Fri, 23 Sep 2022 19:35:03 UTC (24,572 KB)
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