@Article{AAM-39-3, author = {Jianguo, Huang and Sen, Lin and Yue, Yu}, title = {A New Locking-Free Virtual Element Method for Linear Elasticity Problems}, journal = {Annals of Applied Mathematics}, year = {2023}, volume = {39}, number = {3}, pages = {352--384}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0024}, url = {https://global-sci.com/article/72618/a-new-locking-free-virtual-element-method-for-linear-elasticity-problems} }