Volume 39, Issue 1
Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations

Huaijun Yang, Dongyang Shi & Qian Liu

J. Comp. Math., 39 (2021), pp. 63-80.

Published online: 2020-09

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  • 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 demonstrated the theoretical analysis.

  • Keywords

Navier-Stokes equations, Nonconforming MFEM, Supercloseness and superconvergence.

  • AMS Subject Headings

65N38, 65N30, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yhjfhw@163.com (Huaijun Yang)

shi_dy@zzu.edu.cn (Dongyang Shi)

lylq1990@163.com (Qian Liu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-63, author = {Yang , Huaijun and Shi , Dongyang and Liu , Qian }, title = {Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {1}, pages = {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 demonstrated the theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1907-m2018-0263}, url = {http://global-sci.org/intro/article_detail/jcm/18278.html} }
TY - JOUR T1 - Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations AU - Yang , Huaijun AU - Shi , Dongyang AU - Liu , Qian JO - Journal of Computational Mathematics VL - 1 SP - 63 EP - 80 PY - 2020 DA - 2020/09 SN - 39 DO - http://doi.org/10.4208/jcm.1907-m2018-0263 UR - https://global-sci.org/intro/article_detail/jcm/18278.html KW - Navier-Stokes equations, Nonconforming MFEM, Supercloseness and superconvergence. AB -

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 demonstrated the theoretical analysis.

Huaijun Yang, Dongyang Shi & Qian Liu. (2020). Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations. Journal of Computational Mathematics. 39 (1). 63-80. doi:10.4208/jcm.1907-m2018-0263
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