Instance optimality of the adaptive maximum strategy
Numerical Analysis
2017-03-22 v2
Abstract
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of the energy error and the oscillation. This result will be derived in the model setting of Poisson's equation on a polygon, linear finite elements, and conforming triangulations created by newest vertex bisection.
Cite
@article{arxiv.1306.0377,
title = {Instance optimality of the adaptive maximum strategy},
author = {Lars Diening and Christian Kreuzer and Rob Stevenson},
journal= {arXiv preprint arXiv:1306.0377},
year = {2017}
}