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Volume 22, Issue 1
A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization

Yinnian He

J. Comp. Math., 22 (2004), pp. 21-32.

Published online: 2004-02

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  • Abstract

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.  

  • Keywords

Navier-Stokes equations, Mixed finite element, Error estimate, Finite element method.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-21, author = {He , Yinnian}, title = {A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {21--32}, abstract = {

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8848.html} }
TY - JOUR T1 - A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization AU - He , Yinnian JO - Journal of Computational Mathematics VL - 1 SP - 21 EP - 32 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8848.html KW - Navier-Stokes equations, Mixed finite element, Error estimate, Finite element method. AB -

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.  

He , Yinnian. (2004). A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization. Journal of Computational Mathematics. 22 (1). 21-32. doi:
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