The Nonconforming Crouzeix-Raviart Element Approximation and Two-Grid Discretizations for the Elastic Eigenvalue Problem
Year: 2023
Author: Hai Bi, Xuqing Zhang, Yidu Yang
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1041–1063
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2020-0128
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1041–1063
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Elastic eigenvalue problem Nonconforming Crouzeix-Raviart element Two-grid discretizations Error estimates Locking-free.
Author Details
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