Superconvergent gradient recovery for virtual element methods
Hailong Guo, Cong Xie, Ren Zhao
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2019
Virtual element method is a new promising finite element method using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover the superconvergent property of virtual element methods by doing some local post-processing only on the degrees of freedom. Using the linear virtual element method as an example, we propose a universal gradient recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal meshes. Its capability of serving as a posteriori error estimators in adaptive computation is also investigated. Compared to the existing..View full abstract
Guo was partially supported by the Andrew Sisson Fund of the University of Melbourne. Xie was supported by the Postdoctoral International Exchange Program. The authors thank the anonymous referees for their comments and suggestions which significantly improve the quality of this paper.