Year: 2020
Author: Rong An, Can Zhou, Jian Su
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 362–385
Abstract
In this paper, we present a rigorous error analysis of a new higher order fractional-step scheme for approximation of the time-dependent Navier-Stokes equations. The main feature of the proposed scheme is twofold. First, it is a two-step scheme in which the incompressibility and nonlinearities are split. Second, this scheme is a linear scheme and is simple to implement. It is shown that the proposed scheme possesses the convergence rate $\mathcal O((\Delta t)^{3/2})$ in the discrete $l^2$(H$_0^1)\cap$ $l^\infty$(L$^2$)-norm for the end-of-step velocity. Two different numerical experiments are presented to confirm the theoretical analysis and the efficiency of the proposed scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0258
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 362–385
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Incompressible Navier-Stokes equations fractional-step method Crank-Nicolson scheme temporal errors estimates.