The supercloseness property and global superconvergence analysis for the transient conduction-convection equations

Liuchao Xiao, Minghao Li, Zhenzhen Li and Hongru Chen

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: In this paper, we consider the implicit Euler scheme of the transient conduction-convection equations. The supercloseness properties and global superconvergence results are derived for two pairs of low order rectangular elements. Firstly, we obtain a prior estimate of finite element solutions. Then using the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the H−1-norm estimate, we deduce the supercloseness properties of the velocity and temperature in L∞(H1)-norm, and the pressure in L∞(L2)-norm. Next, the global superconvergence results are obtained through the interpolation postprocessing technique. Finally, a numerical example is provided to confirm the theoretical analysis. Compared with previous results, the superconvergence analysis is more concise, a lower regularity of solutions is required, and no time step restriction is needed.

Keywords: Conduction-convection equations; Supercloseness and superconvergence; Stokes projection (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000694

DOI: 10.1016/j.amc.2025.129342

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