Dashti, Masoumeh and Robinson, James C. (James Cooper), 1969-. (2008) An a posteriori condition on the numerical approximations of the Navier–Stokes equations for the existence of a strong solution. SIAM Journal on Numerical Analysis, Vol.46 (No.6). pp. 3136-3150. ISSN 0036-1429

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Abstract

In their 2006 paper, Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. prove that a sufficiently smooth strong solution of the 3D Navier-Stokes equations is robust with respect to small enough changes in initial conditions and forcing function. They also show that if a regular enough strong solution exists, then Galerkin approximations converge to it. They then use these results to conclude that the existence of a sufficiently regular strong solution can be verified using sufficiently refined numerical computations. In this paper we study the strong solutions with less regularity than those considered in Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. We prove a similar robustness result and show the validity of the results relating convergent numerical computations and the existence of the strong solutions.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Navier-Stokes equations
Journal or Publication Title:	SIAM Journal on Numerical Analysis
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1429
Date:	2008
Volume:	Vol.46
Number:	No.6
Number of Pages:	15
Page Range:	pp. 3136-3150
Identification Number:	10.1137/060677537
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Royal Society (Great Britain), Leverhulme Trust (LT), University of Warwick Postgraduate Research Scholarship
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URI:	http://wrap.warwick.ac.uk/id/eprint/29045

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