Recovery-based error estimator for the natural-convection problem based on penalized finite element method
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 9 October 2019
Issue publication date: 21 November 2019
Abstract
Purpose
This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method.
Design/methodology/approach
The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution.
Findings
The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.
Originality/value
The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.
Keywords
Acknowledgements
The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper.
Citation
Li, L., Su, H., Zhao, J. and Feng, X. (2019), "Recovery-based error estimator for the natural-convection problem based on penalized finite element method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 12, pp. 4850-4874. https://doi.org/10.1108/HFF-03-2019-0184
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited