This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.
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.
The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates.
Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.
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).
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
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