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.
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