A simple and effective gradient recovery scheme and a posteriori error estimator for the Virtual Element Method (VEM)

This paper introduces a general recovery-based a posteriori error estimation framework for the Virtual Element Method (VEM) of arbitrary order on general polygonal/polyhedral meshes. The framework consists of a gradient recovery scheme and a posteriori error estimator based on the recovered displacement gradient. A skeletal error, which accurately mimics the behavior of the L ² error of the displacement gradient by only sampling the displacement gradient on the mesh skeleton, is introduced. Through numerical studies on various polygonal/polyhedral meshes, we demonstrate that the proposed gradient recovery scheme can produce considerably more accurate displacement gradient than the original VEM solutions, and that the a posteriori error estimator is able to accurately capture both local and global errors without the knowledge of exact solutions.