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

Author

Listed:
  • Xiao, Liuchao
  • Li, Minghao
  • Li, Zhenzhen
  • Chen, Hongru

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.

Suggested Citation

  • Xiao, Liuchao & Li, Minghao & Li, Zhenzhen & Chen, Hongru, 2025. "The supercloseness property and global superconvergence analysis for the transient conduction-convection equations," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    • Handle: RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000694
    DOI: 10.1016/j.amc.2025.129342
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