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Characteristic stabilized finite element method for non-stationary conduction-convection problems

Yongshuai Wang (School of Mathematical Sciences, East China Normal University, Shanghai, China)
Md. Abdullah Al Mahbub (School of Mathematical Sciences, East China Normal University, Shanghai, China)
Haibiao Zheng (School of Mathematical Sciences, East China Normal University, Shanghai, China and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 29 August 2019

Issue publication date: 16 January 2020

Abstract

Purpose

This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

Design/methodology/approach

To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P1-P1-P1 and P1-P0-P1 triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw.

Findings

The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates.

Originality/value

Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

Keywords

Acknowledgements

Disclosure statement: No potential conflict of interest was reported by the authors.

Y. Wang is supported by East China Normal University Graduate Student Visiting Fund (Project B). M.A.A. Mahbub is partially supported by NSF of China (Grant No. 11571115). H. Zheng is partially supported by NSF of China (Grant Nos. 11771337 and 11971174), SF of Shanghai (Grant No. 19ZR1414300) and Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

Citation

Wang, Y., Mahbub, M.A.A. and Zheng, H. (2020), "Characteristic stabilized finite element method for non-stationary conduction-convection problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 2, pp. 625-658. https://doi.org/10.1108/HFF-04-2019-0318

Publisher

:

Emerald Publishing Limited

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