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An a posteriori condition on the numerical approximations of the Navier–Stokes equations for the existence of a strong solution

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Dashti, Masoumeh and Robinson, James C. (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. doi:10.1137/060677537

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Official URL: http://dx.doi.org/10.1137/060677537

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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, Engineering and Medicine > 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
Official Date: 2008
Dates:
DateEvent
2008Published
Volume: Vol.46
Number: No.6
Number of Pages: 15
Page Range: pp. 3136-3150
DOI: 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

Data sourced from Thomson Reuters' Web of Knowledge

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