Lower a posteriori error estimates on anisotropic meshes
Numerical Analysis
2020-03-03 v4 Numerical Analysis
Abstract
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper [N. Kopteva, Numer. Math., 137 (2017), 607-642] is efficient on certain anisotropic meshes.
Cite
@article{arxiv.1906.05703,
title = {Lower a posteriori error estimates on anisotropic meshes},
author = {Natalia Kopteva},
journal= {arXiv preprint arXiv:1906.05703},
year = {2020}
}
Comments
A few misprints are corrected (and highlighted in blue), and an appendix is included in this version