TY - JOUR
T1 - A New Locking-Free Virtual Element Method for Linear Elasticity Problems
AU - Huang , Jianguo
AU - Lin , Sen
AU - Yu , Yue
JO - Annals of Applied Mathematics
VL - 3
SP - 352
EP - 384
PY - 2023
DA - 2023/09
SN - 39
DO - http://doi.org/10.4208/aam.OA-2023-0024
UR - https://global-sci.org/intro/article_detail/aam/21997.html
KW - Virtual element method, linear elasticity, locking-free, numerical tests.
AB - <p style="text-align: justify;">This paper devises a new lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one $\widetilde{K}$ with additional vertices consisting of interior points on edges of $K$, so that the discrete admissible space is taken as the $V_1$ type virtual element space related to the partition $\{\widetilde{K}\}$ instead of $\{K\}$. The method is proved to converge with optimal convergence order both in $H^1$ and $L^2$ norms and uniformly with respect to the Lamé constant $\lambda$. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.</p>