Hybridization of the Virtual Element Method for linear elasticity problems

TL;DR

This paper extends the hybridization technique to the Virtual Element Method for 2D and 3D linear elasticity problems, improving displacement approximation and confirming effectiveness through numerical experiments.

Contribution

It introduces a hybridization approach for VEM in elasticity, enhancing displacement approximation with a simple post-processing method.

Findings

Numerical results confirm the theoretical convergence in 2D and 3D.

The post-processing improves displacement field accuracy.

The method is adaptable to various dimensions and problem types.

Abstract

We extend the hybridization procedure proposed in [Arnold, Brezzi, 1985, ESAIM: M2AN] to the Virtual Element Method for linear elasticity problems based on the Hellinger-Reissner principle. To illustrate such a technique, we focus on the 2D case, but other methods and 3D problems can be considered as well. We also show how to design a better approximation of the displacement field using a straightforward post-processing procedure. The numerical experiments confirm the theory for both two and three-dimensional problems.