Year: 2021
Author: Yaoyao Chen, Yunqing Huang, Yidan Zhang, Nianyu Yi, Yaoyao Chen, Yunqing Huang, Nianyu Yi
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 508–526
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0117
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 508–526
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Crouzeix-Raviart element gradient recovery superconvergent cluster recovery.