Volume 39, Issue 3
A New Locking-Free Virtual Element Method for Linear Elasticity Problems

Jianguo Huang, Sen Lin & Yue Yu

Ann. Appl. Math., 39 (2023), pp. 352-384.

Published online: 2023-09

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  • 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.

  • AMS Subject Headings

65N30, 65N12, 65N15

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COPYRIGHT: © Global Science Press

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@Article{AAM-39-352, author = {Huang , JianguoLin , Sen and Yu , Yue}, 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 = {http://global-sci.org/intro/article_detail/aam/21997.html} }
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 -

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.

Huang , JianguoLin , Sen and Yu , Yue. (2023). A New Locking-Free Virtual Element Method for Linear Elasticity Problems. Annals of Applied Mathematics. 39 (3). 352-384. doi:10.4208/aam.OA-2023-0024
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