Residual estimates for post-processors in elliptic problems
Numerical Analysis
2023-03-01 v2 Numerical Analysis
Abstract
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques to enable efficient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge. We showcase our results by applying them to two classes of very popular reconstruction operators, the Smoothness-Increasing Accuracy-Enhancing filter and Superconvergent Patch Recovery. Extensive numerical tests are conducted that confirm our analytic findings.
Cite
@article{arxiv.1906.04658,
title = {Residual estimates for post-processors in elliptic problems},
author = {Andreas Dedner and Jan Giesselmann and Tristan Pryer and Jennifer K Ryan},
journal= {arXiv preprint arXiv:1906.04658},
year = {2023}
}
Comments
25 pages, 17 figures