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Volume 39, Issue 1
Mixed Finite Element Methods for Fractional Navier-Stokes Equations

Xiaocui Li & Xu You

DOI: 10.4208/jcm.1911-m2018-0153

J. Comp. Math., 39 (2021), pp. 130-146.

Published online: 2020-09

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  • Abstract

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations. The proposed method is based on the mixed finite element method in space and a finite difference scheme in time. The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail. Furthermore, We give the convergence analysis for both semidiscrete and fully discrete schemes and then prove that the numerical solution converges the exact one with order $O(h^2+k)$, where $h$ and $k$ respectively denote the space step size and the time step size. Finally, numerical examples are presented to demonstrate the effectiveness of our numerical methods.

  • Keywords

Time-fractional Navier-Stokes equations, Finite element method, Error estimates, Strong convergence.

  • AMS Subject Headings

60N15, 65M60, 60N30, 75D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

anny9702@126.com (Xiaocui Li)

youxu@bipt.edu.cn (Xu You)

  • BibTex
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  • TXT
@Article{JCM-39-130, author = {Li , Xiaocui and You , Xu}, title = {Mixed Finite Element Methods for Fractional Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {1}, pages = {130--146}, abstract = {

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations. The proposed method is based on the mixed finite element method in space and a finite difference scheme in time. The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail. Furthermore, We give the convergence analysis for both semidiscrete and fully discrete schemes and then prove that the numerical solution converges the exact one with order $O(h^2+k)$, where $h$ and $k$ respectively denote the space step size and the time step size. Finally, numerical examples are presented to demonstrate the effectiveness of our numerical methods.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1911-m2018-0153}, url = {http://global-sci.org/intro/article_detail/jcm/18281.html} }
TY - JOUR T1 - Mixed Finite Element Methods for Fractional Navier-Stokes Equations AU - Li , Xiaocui AU - You , Xu JO - Journal of Computational Mathematics VL - 1 SP - 130 EP - 146 PY - 2020 DA - 2020/09 SN - 39 DO - http://doi.org/10.4208/jcm.1911-m2018-0153 UR - https://global-sci.org/intro/article_detail/jcm/18281.html KW - Time-fractional Navier-Stokes equations, Finite element method, Error estimates, Strong convergence. AB -

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations. The proposed method is based on the mixed finite element method in space and a finite difference scheme in time. The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail. Furthermore, We give the convergence analysis for both semidiscrete and fully discrete schemes and then prove that the numerical solution converges the exact one with order $O(h^2+k)$, where $h$ and $k$ respectively denote the space step size and the time step size. Finally, numerical examples are presented to demonstrate the effectiveness of our numerical methods.

Li , Xiaocui and You , Xu. (2020). Mixed Finite Element Methods for Fractional Navier-Stokes Equations. Journal of Computational Mathematics. 39 (1). 130-146. doi:10.4208/jcm.1911-m2018-0153
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