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Journal of Computational Mathematics ›› 2021, Vol. 39 ›› Issue (1): 63-80.DOI: 10.4208/jcm.1907-m2018-0263

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SUPERCONVERGENCE ANALYSIS OF LOW ORDER NONCONFORMING MIXED FINITE ELEMENT METHODS FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS

Huaijun Yang1, Dongyang Shi2, Qian Liu2   

  1. 1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2018-12-02 Revised:2019-05-12 Online:2021-01-15 Published:2021-03-11
  • Supported by:
    This work is supported by National Natural Science Foundation of China (Nos. 11671369; 11271340).
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Huaijun Yang, Dongyang Shi, Qian Liu. SUPERCONVERGENCE ANALYSIS OF LOW ORDER NONCONFORMING MIXED FINITE ELEMENT METHODS FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(1): 63-80.

In this paper, the superconvergence properties of the time-dependent Navier-Stokes equations are investigated by a low order nonconforming mixed finite element method (MFEM). In terms of the integral identity technique, the superclose error estimates for both the velocity in broken H1-norm and the pressure in L2-norm are first obtained, which play a key role to bound the numerical solution in L∞-norm. Then the corresponding global superconvergence results are derived through a suitable interpolation postprocessing approach. Finally, some numerical results are provided to demonstrated the theoretical analysis.
Key words: Navier-Stokes equations, Nonconforming MFEM, Supercloseness and superconvergence

CLC Number: 

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