English

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 hphp 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 hphp adaptive mesh refinements for very general polygonal meshes. In addition, a novel VEM hphp 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.

Keywords

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

R2 v1 2026-06-23T01:30:51.073Z