Abstract
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 L2 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. We also demonstrate the use of the VEM skeletal error estimators to guide adaptive mesh refinement.
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