An a posteriori condition on the numerical approximations of the Navier–Stokes equations for the existence of a strong solution
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 0036-1429Full text not available from this repository.
Official URL: http://dx.doi.org/10.1137/060677537
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|
|Number of Pages:||15|
|Page Range:||pp. 3136-3150|
|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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