TY - JOUR
T1 - The Nonconforming Crouzeix-Raviart Element Approximation and Two-Grid Discretizations for the Elastic Eigenvalue Problem
AU - Bi , Hai
AU - Zhang , Xuqing
AU - Yang , Yidu
JO - Journal of Computational Mathematics
VL - 6
SP - 1041
EP - 1063
PY - 2023
DA - 2023/11
SN - 41
DO - http://doi.org/10.4208/jcm.2201-m2020-0128
UR - https://global-sci.org/intro/article_detail/jcm/22103.html
KW - Elastic eigenvalue problem, Nonconforming Crouzeix-Raviart element, Two-grid discretizations, Error estimates, Locking-free.
AB - <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>