A Posteriori Error Estimates for the Virtual Element Method for the Stokes Problem

This paper presents a residual-type a posteriori error estimator for the virtual element method for the Stokes problem. It is proved that the a posteriori error estimator is reliable and efficient. The virtual element method allows the use of very general polygonal meshes and handles the hanging nodes naturally. Consequently, the local post-processing of locally adapted mesh can be avoided, which simplifies the adaptive procedure. A series of numerical examples are reported to show the effectiveness of adaptive mesh refinement driven by this estimator.