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A symmetric error estimate for Galerkin approximations of time-dependent Navier-Stokes equations in two dimensions

Authors: Todd F. Dupont and Itir Mogultay
Journal: Math. Comp. 78 (2009), 1919-1927
MSC (2000): Primary 65M12; Secondary 65M60
Published electronically: February 16, 2009
MathSciNet review: 2521272
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Abstract: A symmetric error estimate for Galerkin approximations of solutions of the Navier-Stokes equations in two space dimensions plus time is given. The finite-dimensional function spaces are taken to be divergence-free, and time is left continuous. The estimate is similar to known results for scalar parabolic equations. An application of the result is given for mixed method formulations. A short discussion of examples is included. Finally, there are some remarks about a partial extension to three space dimensions.

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Additional Information

Todd F. Dupont
Affiliation: Department of Computer Science, University of Chicago, 1100 East 58th Street, Chicago, Illinois 60637

Itir Mogultay
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Address at time of publication: Yeditepe University, Department of Mathematics, 26 Augustos Yerleskesi Kayisdagi, Caddesi 81120 Kayisdagi, Istanbul Turkey

Keywords: Error estimates, Navier-Stokes equations, Galerkin approximation, quasi-optimal
Received by editor(s): July 30, 2007
Received by editor(s) in revised form: November 9, 2008
Published electronically: February 16, 2009
Additional Notes: The work of the authors was supported in part by the ASC Flash Center at the University of Chicago which is funded by the U. S. Department of Energy under contract B523820.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.