A posteriori error estimation and adaptivity in $hp$ virtual elements
Numerical Analysis
2019-06-21 v2 Numerical Analysis
Abstract
An explicit and computable error estimator for the version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide adaptive mesh refinements for very general polygonal meshes. In addition, a novel VEM Cl\'ement quasi-interpolant, instrumental for the a posteriori error analysis, is introduced. The performances of the adaptive method are validated by a number of numerical experiments.
Cite
@article{arxiv.1804.07898,
title = {A posteriori error estimation and adaptivity in $hp$ virtual elements},
author = {L. Beirão da Veiga and G. Manzini and L. Mascotto},
journal= {arXiv preprint arXiv:1804.07898},
year = {2019}
}
Comments
28 pages, 16 figures