Introduction to the Virtual Element Method for 2D Elasticity

TL;DR

This paper introduces the virtual element method (VEM) for 2D elasticity, focusing on implementation, derivations, and practical examples to aid researchers in adopting and verifying the technique.

Contribution

It provides an accessible introduction to VEM for 2D elasticity, emphasizing implementation details and practical numerical results.

Findings

VEM effectively solves 2D elasticity problems.

Implementation guidelines facilitate adoption of VEM.

Numerical examples demonstrate VEM's utility.

Abstract

An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems is assumed. Derivations relevant to successful implementation are covered. Some theory is covered, but the focus here is on implementation and results. Examples are given that illustrate the utility of the method. Numerical results are provided to help researchers implement and verify their own results.