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Volume 30, Issue 6
A Stabilized Equal-Order Finite Volume Method for the Stokes Equations

Wanfu Tian, Liqiu Song & Yonghai Li

DOI: 10.4208/jcm.1206-m3843

J. Comp. Math., 30 (2012), pp. 615-628.

Published online: 2012-12

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  • Abstract

We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm. In addition, a second order optimal error estimate for the velocity in the $L^2$ norm is derived. Numerical experiments illustrating the theoretical results are included.

  • Keywords

Stokes equations, Equal-order finite element pair, Finite volume method, Error estimate.

  • AMS Subject Headings

65N08, 65N15, 65N30, 76D05.

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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  • TXT
@Article{JCM-30-615, author = {Wanfu Tian, Liqiu Song and Yonghai Li}, title = {A Stabilized Equal-Order Finite Volume Method for the Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {6}, pages = {615--628}, abstract = {

We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm. In addition, a second order optimal error estimate for the velocity in the $L^2$ norm is derived. Numerical experiments illustrating the theoretical results are included.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1206-m3843}, url = {http://global-sci.org/intro/article_detail/jcm/8455.html} }
TY - JOUR T1 - A Stabilized Equal-Order Finite Volume Method for the Stokes Equations AU - Wanfu Tian, Liqiu Song & Yonghai Li JO - Journal of Computational Mathematics VL - 6 SP - 615 EP - 628 PY - 2012 DA - 2012/12 SN - 30 DO - http://doi.org/10.4208/jcm.1206-m3843 UR - https://global-sci.org/intro/article_detail/jcm/8455.html KW - Stokes equations, Equal-order finite element pair, Finite volume method, Error estimate. AB -

We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm. In addition, a second order optimal error estimate for the velocity in the $L^2$ norm is derived. Numerical experiments illustrating the theoretical results are included.

Wanfu Tian, Liqiu Song and Yonghai Li. (2012). A Stabilized Equal-Order Finite Volume Method for the Stokes Equations. Journal of Computational Mathematics. 30 (6). 615-628. doi:10.4208/jcm.1206-m3843
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