Hybridization of the virtual element method for linear elasticity problems

In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed nonconforming finite element methods: Implementation, postprocessing error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7–32] to Virtual Element Method for linear elasticity problems based on Hellinger–Reissner principle. To illustrate such a technique, focus specific 2D scheme, but other methods 3D can be considered as well. We also show how design better approximation of displacement field using straightforward post-processing procedure. The numerical experiments confirm theory both two three-dimensional problems.