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Error analysis of fully discrete velocity-correction methods for incompressible flows

Authors: J. L. Guermond, Jie Shen and Xiaofeng Yang
Journal: Math. Comp. 77 (2008), 1387-1405
MSC (2000): Primary 65M12, 35Q30, 35J05, 76D05
Published electronically: March 7, 2008
MathSciNet review: 2398773
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Abstract: A fully discrete version of the velocity-correction method, proposed by Guermond and Shen (2003) for the time-dependent Navier-Stokes equations, is introduced and analyzed. It is shown that, when accounting for space discretization, additional consistency terms, which vanish when space is not discretized, have to be added to establish stability and optimal convergence. Error estimates are derived for both the standard version and the rotational version of the method. These error estimates are consistent with those by Guermond and Shen (2003) as far as time discretiztion is concerned and are optimal in space for finite elements satisfying the inf-sup condition.

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Additional Information

J. L. Guermond
Affiliation: Department of Mathematics, Texas A$&$M University, College Station, Texas 77843

Jie Shen
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Xiaofeng Yang
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599

Keywords: Navier-Stokes equations, velocity-correction, projection methods, finite element methods, spectral methods, incompressibility, fraction step methods
Received by editor(s): December 29, 2006
Received by editor(s) in revised form: June 3, 2007
Published electronically: March 7, 2008
Additional Notes: The work of the first author was supported in part by NSF DMS-0510650
The work of the second and third authors was supported in part by NSF DMS-0509665 and DMS-0610646
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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