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

Heng Chi, Lourenço Beirão da Veiga, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)21-58
Number of pages38
JournalComputer Methods in Applied Mechanics and Engineering
Volume347
DOIs
StatePublished - Apr 15 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Keywords

  • Element skeleton
  • Error estimation
  • Gradient recovery
  • Higher order
  • Mesh skeleton
  • Virtual element method (VEM)

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