Comparison of standard and stabilization free Virtual Elements on anisotropic elliptic problems

TL;DR

This paper compares standard Virtual Element Methods (VEM) and stabilization free E^2VEM for anisotropic elliptic problems, showing that E^2VEM can reduce errors and improve convergence without stabilizing terms.

Contribution

It introduces and evaluates stabilization free E^2VEM, demonstrating its advantages over standard VEM in anisotropic elliptic problems.

Findings

E^2VEM reduces error magnitude compared to standard VEM.

E^2VEM improves convergence on polygonal meshes.

Avoiding stabilization can be beneficial for anisotropic problems.

Abstract

In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E$^2$VEM) with the focus on some elliptic test problems whose solution and diffusivity tensor are characterized by anisotropies. Results show that the possibility to avoid an arbitrary stabilizing part, offered by E$^2$VEM methods, can reduce the magnitude of the error on general polygonal meshes and help convergence.