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.
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