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 language | English (US) |
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Pages (from-to) | 21-58 |
Number of pages | 38 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 347 |
DOIs | |
State | Published - Apr 15 2019 |
Externally published | Yes |
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)