A posteriori error estimates for a Virtual Elements Method for the Steklov eigenvalue problem

TL;DR

This paper develops and analyzes an a posteriori error estimator for a virtual element method solving the Steklov eigenvalue problem, enabling efficient adaptive mesh refinement and demonstrating its effectiveness through numerical tests.

Contribution

It introduces a residual-based a posteriori error estimator for the virtual element method applied to the Steklov eigenvalue problem, with proven reliability and efficiency.

Findings

The error estimator effectively guides adaptive mesh refinement.

Numerical tests confirm the estimator's reliability and efficiency.

The method handles general polygonal meshes efficiently.

Abstract

The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing very efficiently mesh refinement strategies. We introduce a residual type a posteriori error estimator and prove its reliability and efficiency. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests, that allow us to assess the performance of this approach.