A posteriori error estimates for a Virtual Elements Method for the Steklov eigenvalue problem
Provides a rigorous error estimation framework for virtual element methods in eigenvalue problems, enabling efficient adaptive mesh refinement for practitioners using polygonal meshes.
The paper develops a residual-type a posteriori error estimator for the virtual element method applied to the Steklov eigenvalue problem, proving its reliability and efficiency, and demonstrates its effectiveness in driving adaptive mesh refinement through numerical tests.
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.