Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping

Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping

Year:    2022

Author:    Minghao Li, Zhenzhen Li, Dongyang Shi

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 248–274

Abstract

In this paper, the transient Navier-Stokes equations with damping are considered. Firstly, the semi-discrete scheme is discussed and optimal error estimates are derived. Secondly, a linearized backward Euler scheme is proposed. By the error split technique, the Stokes operator and the $H^{-1}$-norm estimate, unconditional optimal error estimates for the velocity in the norms ${L^\infty}(L^2)$ and ${L^\infty}(H^1)$, and the pressure in the norm ${L^\infty}(L^2)$ are deduced. Finally, two numerical examples are provided to confirm the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0239

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 248–274

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Navier-Stokes equations with damping linearized backward Euler scheme error splitting technique unconditional optimal error estimates.

Author Details

Minghao Li

Zhenzhen Li

Dongyang Shi

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