@Article{JCM-41-1041,
author = {Bi , HaiZhang , Xuqing and Yang , Yidu},
title = {The Nonconforming Crouzeix-Raviart Element Approximation and Two-Grid Discretizations for the Elastic Eigenvalue Problem},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {6},
pages = {1041--1063},
abstract = {<p style="text-align: justify;">In this paper, we extend the work of Brenner and Sung [Math. Comp. 59, 321–338
(1992)] and present a regularity estimate for the elastic equations in concave domains.
Based on the regularity estimate we prove that the constants in the error estimates of the
nonconforming Crouzeix-Raviart element approximations for the elastic equations/eigenvalue problem are independent of Lamé constant, which means the nonconforming Crouzeix-Raviart element approximations are locking-free. We also establish two kinds of two-grid
discretization schemes for the elastic eigenvalue problem, and analyze that when the mesh
sizes of coarse grid and fine grid satisfy some relationship, the resulting solutions can
achieve the optimal accuracy. Numerical examples are provided to show the efficiency of
two-grid schemes for the elastic eigenvalue problem.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2201-m2020-0128},
url = {http://global-sci.org/intro/article_detail/jcm/22103.html}
}