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A symmetric error estimate for Galerkin approximations of time-dependent Navier-Stokes equations in two dimensions
Author(s):
Todd
F.
Dupont;
Itir
Mogultay.
Journal:
Math. Comp.
78
(2009),
1919-1927.
MSC (2000):
Primary 65M12;
Secondary 65M60
Posted:
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.
References:
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- 2.
- Susanne C. Brenner and L. Ridgway Scott, The mathematical theory of finite element methods, Springer-Verlag, 2008. MR 2373954 (2008m:65001)
- 3.
- Jim Douglas, Jr. and Todd Dupont, Galerkin methods for parabolic equations, SIAM J. Numer. Anal. 7 (1970), no. 4, 575-626. MR 0277126 (43:2863)
- 4.
- T. F. Dupont, Mesh modification for evolution equations, Mathematics of Computation 36 (1982), 85-107. MR 658215 (84g:65131)
- 5.
- T. F. Dupont and Y. Liu, Symmetric error estimates for moving mesh Galerkin methods for advection-diffusion equations, SIAM J. Numer. Anal. 40 (2002), no. 3, 914-927. MR 1949398 (2004b:65147)
- 6.
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Additional Information:
Todd
F.
Dupont
Affiliation:
Department of Computer Science, University of Chicago, 1100 East 58th Street, Chicago, Illinois 60637
Email:
t-dupont@uchicago.edu
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
Email:
imogulta@cs.uchicago.edu
DOI:
10.1090/S0025-5718-09-02243-1
PII:
S 0025-5718(09)02243-1
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
Posted:
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.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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