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

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 (cid:101) 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 { (cid:101) 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 Lam´e constant λ . Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.