A novel locking-free virtual element method for linear elasticity problems

12/27/2021

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by   Jianguo Huang, et al.

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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 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 {K} instead of {K}. The method is shown to be uniformly convergent with the optimal rates both in H^1 and L^2 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.