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Timestepping schemes for the 3d Navier-Stokes equations.

Hong, Y-J and Wirosoetisno, D (2015) 'Timestepping schemes for the 3d Navier-Stokes equations.', Applied numerical mathematics., 96 . pp. 153-164.

Abstract

It is well known that the (exact) solutions of the 3d Navier–Stokes equations remain bounded for all time if the initial data and the forcing are sufficiently small relative to the viscosity. They also remain bounded for a finite time for arbitrary initial data in L2. In this article, we consider two temporal discretisations (semi-implicit and fully implicit) of the 3d Navier–Stokes equations in a periodic domain and prove that their solutions remain uniformly bounded in H1 subject to essentially the same respective smallness conditions as the continuous system (on initial data and forcing or on the time of existence) provided the time step is small.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.apnum.2015.05.006
Publisher statement:© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:03 May 2015
Date deposited:13 September 2017
Date of first online publication:05 June 2015
Date first made open access:No date available

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