A residual a posteriori error estimate for the Stabilization-free Virtual Element Method

TL;DR

This paper develops an a posteriori error estimator for stabilization-free virtual element methods applied to the 2D Poisson problem, demonstrating its effectiveness and robustness across various mesh types and diffusion jumps.

Contribution

It introduces a novel a posteriori error analysis for stabilization-free virtual element methods, establishing equivalence with residual estimators without stabilization.

Findings

Estimator accurately predicts errors across different meshes

Method remains robust with diffusion coefficient jumps

Numerical experiments confirm theoretical results

Abstract

In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mesh types, and robustness with respect to jumps of the diffusion term.