A virtual element method for the elasticity problem allowing small edges

TL;DR

This paper introduces a virtual element method for 2D elasticity problems that accommodates meshes with small edges and only requires star-shaped polygons, providing error estimates and numerical validation.

Contribution

The paper develops a virtual element method that relaxes traditional mesh assumptions, allowing small edges and star-shaped polygons, with detailed error analysis including Lamé constants.

Findings

Error estimates demonstrate robustness of the method.

Numerical tests confirm the method's effectiveness.

Relaxed mesh assumptions improve flexibility in elasticity simulations.

Abstract

In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In particular, we consider only star-shaped polygons for the meshes. Suitable error estimates are presented, where a rigorous analysis on the influence of the Lam\'e constants in each estimate is presented. We report numerical tests to assess the performance of the method.