@Article{NMTMA-14-508,
author = {Zhang , YidanChen , YaoyaoHuang , Yunqing and Yi , Nianyu},
title = {Superconvergent Cluster Recovery Method for the Crouzeix-Raviart Element},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {2},
pages = {508--526},
abstract = {<p style="text-align: justify;">In this paper, we propose and numerically investigate a superconvergent
cluster recovery (SCR) method for the Crouzeix-Raviart (CR) element. The proposed
recovery method reconstructs a $C^0$ linear gradient. A linear polynomial approximation is obtained by a least square fitting to the CR element approximation at certain
sample points, and then taken derivatives to obtain the recovered gradient. The SCR
recovery operator is superconvergent on uniform mesh of four patterns. Numerical
examples show that SCR can produce a superconvergent gradient approximation for
the CR element, and provide an asymptotically exact error estimator in the adaptive
CR finite element method.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0117},
url = {http://global-sci.org/intro/article_detail/nmtma/18609.html}
}