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

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