Weak Galerkin method for the Navier-Stokes equation with nonlinear damping term

Yue Tai; Xiuli Wang; Weishi Yin; Pinchao Meng; Yue Tai; Xiuli Wang; Weishi Yin; Pinchao Meng

doi:10.3934/nhm.2024021

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 475-499. doi: 10.3934/nhm.2024021

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Research article

Weak Galerkin method for the Navier-Stokes equation with nonlinear damping term

1.
School of Mathematics and Statistics, Changchun University of Science and Technology, 7089. Weixing Rd, Changchun, Jilin 130022, China
2.
Department of Mathematics, Jilin University, 2699. Qianjin Ave, Changchun, Jilin 130012, China

Received: 29 December 2023 Revised: 03 April 2024 Accepted: 23 April 2024 Published: 28 April 2024

The primary focus of this research was to investigate the weak Galerkin (WG) finite element method for the Navier-Stokes equations with damping. We established the weak Galerkin finite element numerical scheme and demonstrated the existence and uniqueness of the weak Galerkin numerical solution. Additionally, optimal errors estimates for the velocity and pressure were obtained. Eventually, numerous numerical examples were reported to validate the theoretical analysis.
- weak Galerkin finite element method,
- discrete weak gradient,
- Navier-Stokes equation,
- nonlinear term
Citation: Yue Tai, Xiuli Wang, Weishi Yin, Pinchao Meng. Weak Galerkin method for the Navier-Stokes equation with nonlinear damping term[J]. Networks and Heterogeneous Media, 2024, 19(2): 475-499. doi: 10.3934/nhm.2024021

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Abstract

The primary focus of this research was to investigate the weak Galerkin (WG) finite element method for the Navier-Stokes equations with damping. We established the weak Galerkin finite element numerical scheme and demonstrated the existence and uniqueness of the weak Galerkin numerical solution. Additionally, optimal errors estimates for the velocity and pressure were obtained. Eventually, numerous numerical examples were reported to validate the theoretical analysis.

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