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.
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