THE NONCONFORMING CROUZEIX-RAVIART ELEMENT APPROXIMATION AND TWO-GRID DISCRETIZATIONS FOR THE ELASTICEIGENVALUE PROBLEM  

作　　者：Hai Bi Xuqing Zhang Yidu Yang 

机构地区：[1]School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China [2]School of Biology&Engineering,Guizhou Medical University,GuiYang 550025,China

出　　处：《Journal of Computational Mathematics》2023年第6期1041-1063,共23页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China (Grant No.11761022)。

摘　　要：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 Laméconstant,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.

关 键 词：Elastic eigenvalue problem Nonconforming Crouzeix-Raviart element Two-grid discretizations Error estimates LOCKING-FREE 

分 类 号：O241.82[理学—计算数学]