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arXiv · 2301.01401

Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations

Xiaoli Li·Jie Shen
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Abstract

We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent splitting scheme coupled with a generalized scalar auxiliary variable (GSAV) approach for the Navier-Stokes equations with no-slip boundary conditions. The scheme is linear, unconditionally stable, and only requires solving a sequence of Poisson type equations at each time step. By using the build-in unconditional stability of the GSAV approach, we derive optimal global (resp. local) in time error estimates in the two (resp. three) dimensional case for the velocity and pressure approximations.

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Xiaoli Li, Jie Shen. 2023-01-04. Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations. https://arxiv.org/abs/2301.01401

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