Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations

Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations

Year:    2021

Author:    Huaijun Yang, Dongyang Shi, Qian Liu

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 63–80

Abstract

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 $H^1$-norm and the pressure in $L^2$-norm are first obtained, which play a key role to bound the numerical solution in $L^{\infty}$-norm. Then the corresponding global superconvergence results are derived through a suitable interpolation postprocessing approach. Finally, some numerical results are provided to demonstrate the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1907-m2018-0263

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 63–80

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Navier-Stokes equations Nonconforming MFEM Supercloseness and superconvergence.

Author Details

Huaijun Yang

Dongyang Shi

Qian Liu

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