Virtual Element Methods on Meshes with Small Edges or Faces

TL;DR

This paper analyzes the accuracy of virtual element methods applied to Poisson problems on complex meshes with small edges or faces, providing error estimates for such challenging geometries.

Contribution

It introduces error estimates for virtual element methods on meshes with small edges or faces, extending their applicability to more complex geometries.

Findings

Error estimates are established for meshes with small edges or faces.

Virtual element methods remain accurate on complex polygonal/polyhedral meshes.

The results improve understanding of VEM performance on irregular meshes.

Abstract

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).