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arXiv · 2507.01296

Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations

Fukeng Huang·Jie Shen
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Abstract

A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+β}$ with $β\ge 1$ being a free parameter. It is shown that by choosing {\color{black} $β= 3, \,6,\,9$} respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. {\color{black}These } results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual BDF (i.e. $β=1$) are not unconditionally stable while the new third- and fourth-order schemes with suitable $β$ are unconditionally stable and lead to expected convergence rates.

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Fukeng Huang, Jie Shen. 2025-07-02. Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations. https://arxiv.org/abs/2507.01296

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