Stabilization-free virtual element method for plane elasticity

TL;DR

This paper introduces a first-order virtual element method for plane elasticity that does not require stabilization, demonstrating optimal convergence and robustness through benchmark tests.

Contribution

The paper develops a stabilization-free virtual element method for plane elasticity, providing theoretical analysis and numerical validation of its effectiveness.

Findings

Optimal convergence in $L^2$ norm and energy seminorm

Method is well-posed with established error estimates

Validated on benchmark problems with positive results

Abstract

We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a series of well-known benchmark problems from linear elasticity and numerical results are presented that affirm the optimal convergence rate of the virtual element method in the $L^2$ norm and the energy seminorm.