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Unconditional Superconvergence Error Estimates of Semi-Implicit Low-Order Conforming Mixed Finite Element Method for Time-Dependent Navier–Stokes Equations

Author

Listed:
  • Xiaoling Meng

    (School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China)

  • Huaijun Yang

    (School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China)

Abstract

In this paper, the unconditional superconvergence error analysis of the semi-implicit Euler scheme with low-order conforming mixed finite element discretization is investigated for time-dependent Navier–Stokes equations. In terms of the high-accuracy error estimates of the low-order finite element pair on the rectangular mesh and the unconditional boundedness of the numerical solution in L ∞ -norm, the superclose error estimates for velocity in H 1 -norm and pressure in L 2 -norm are derived firstly by dealing with the trilinear term carefully and skillfully. Then, the global superconvergence results are obtained with the aid of the interpolation post-processing technique. Finally, some numerical experiments are carried out to support the theoretical findings.

Suggested Citation

  • Xiaoling Meng & Huaijun Yang, 2023. "Unconditional Superconvergence Error Estimates of Semi-Implicit Low-Order Conforming Mixed Finite Element Method for Time-Dependent Navier–Stokes Equations," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1945-:d:1128545
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