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Research Progress in the Highly Efficient Fully Discrete Finite Element Method for Solving the 3D Time-Dependent Navier-Stokes Equations

School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830017, China
School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi Xi'an 710049, China
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Abstract

Main difficulties of numerically solving the 3D time-dependent Navier-Stokes equations are incompressibility condition, nonlinearity and longtime integration. First, we discuss the research progress and recent achievements in the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations. Secondly, we expound the stability and error estimates of the finite element spatial discrete solution and the optimal error estimates of the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations.

Keywords

Navier-Stokes equationshighly efficient finite element methodstabilityoptimal error estimate
CLC number: O242.21 Document code: A Article ID: 2096-7675(2022)03-0257-09

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Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 39 Issue 3,
May 2022
Pages 257-265
DOI: 10.13568/j.cnki.651094.651316.2022.04.09.0001

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HE Y, FENG X. Research Progress in the Highly Efficient Fully Discrete Finite Element Method for Solving the 3D Time-Dependent Navier-Stokes Equations. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2022, 39(3): 257-265. https://doi.org/10.13568/j.cnki.651094.651316.2022.04.09.0001

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Received: 09 April 2022
Published: 01 May 2022
© 2022 Journal of Xinjiang University (Natural Science Edition in Chinese and English)