Anisotropic a posteriori error estimate for the Virtual Element Method
Numerical Analysis
2020-01-03 v1 Numerical Analysis
Abstract
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes.
Cite
@article{arxiv.2001.00381,
title = {Anisotropic a posteriori error estimate for the Virtual Element Method},
author = {Paola Francesca Antonietti and Stefano Berrone and Andrea Borio and Alessandro D'Auria and Marco Verani and Steffen Weisser},
journal= {arXiv preprint arXiv:2001.00381},
year = {2020}
}