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A New Locking-Free Virtual Element Method for Linear Elasticity Problems

A New Locking-Free Virtual Element Method for Linear Elasticity Problems

Year:    2023

Author:    Jianguo Huang, Sen Lin, Yue Yu

Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 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 ˜K with additional vertices consisting of interior points on edges of K, so that the discrete admissible space is taken as the V1 type virtual element space related to the partition {˜K} instead of {K}. The method is proved to converge with optimal convergence order both in H1 and L2 norms and uniformly with respect to the Lamé constant λ. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aam.OA-2023-0024

Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 352–384

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Virtual element method linear elasticity locking-free numerical tests.

Author Details

Jianguo Huang Email

Sen Lin Email

Yue Yu Email

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    https://doi.org/10.1016/j.aml.2024.109333 [Citations: 0]