A Stabilized Equal-Order Finite Volume Method for the Stokes Equations

A Stabilized Equal-Order Finite Volume Method for the Stokes Equations

Year:    2012

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1206-m3843

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 615–628

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

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