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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 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/060677537
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: |
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| 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 |
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