The nonconforming virtual element method for elasticity problems

Abstract

We present the nonconforming virtual element method for linear elasticity problems in the pure displacement formulation. This method is uniformly convergent for the nearly incompressible case. The optimal convergence in the H1 norm is proved under some regularity assumptions. We mention that, for the lowest-order case on triangular meshes the nonconforming virtual element method coincides with the nonconforming finite element method presented by Brenner and Sung (1992) [19] up to an approximation of the right-hand side. Besides, we also present the nonconforming virtual element method for the pure traction problem, which is proved to be uniformly convergent with respect to the Lamé constant. Finally, we demonstrate the optimal convergence and stability of the nonconforming virtual element method by some numerical results.