Adv. Appl. Math. Mech., 12 (2020), pp. 362-385.
Published online: 2020-01
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0258}, url = {http://global-sci.org/intro/article_detail/aamm/13626.html} }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.