2021/12/27 by Jianguo Huang, Sen Lin, Huang, Jianguo +3
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2112.13848
openalex publication_date 2021/12/27 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper devises a novel 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 \widetildeK 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 \\widetildeK\ instead of \K\. The method is shown to be uniformly convergent with the optimal rates both in H1 and L2 norms 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.