Volume 14, Issue 1
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping

Minghao Li, Zhenzhen Li & Dongyang Shi

Adv. Appl. Math. Mech., 14 (2022), pp. 248-274.

Published online: 2021-11

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-248, author = {Li , Minghao and Li , Zhenzhen and Shi , Dongyang}, title = {Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {14}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0239}, url = {http://global-sci.org/intro/article_detail/aamm/19984.html} }
TY - JOUR T1 - Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping AU - Li , Minghao AU - Li , Zhenzhen AU - Shi , Dongyang JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 248 EP - 274 PY - 2021 DA - 2021/11 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0239 UR - https://global-sci.org/intro/article_detail/aamm/19984.html KW - Navier-Stokes equations with damping, linearized backward Euler scheme, error splitting technique, unconditional optimal error estimates. AB -

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.

Minghao Li, Zhenzhen Li & Dongyang Shi. (1970). Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping. Advances in Applied Mathematics and Mechanics. 14 (1). 248-274. doi:10.4208/aamm.OA-2020-0239
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