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Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations

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Abstract

In this paper, some local and parallel finite element methods based on two-grid discretizations are proposed and investigated for the unsteady Navier-Stokes equations. The backward Euler scheme is considered for the temporal discretization, and two-grid method is used for the space discretization. The key idea is that for a solution to the unsteady Navier-Stokes problem, we could use a relatively coarse mesh to approximate low-frequency components and use some local fine mesh to compute high-frequency components. Some local a priori estimate is obtained. With that, theoretical results are derived. Finally, some numerical results are reported to support the theoretical findings.

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Funding

This work is subsidized by NSFC (Grant No. 11701343).

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Qingtao Li & Guangzhi Du

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  1. Qingtao Li
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  2. Guangzhi Du
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Correspondence to Guangzhi Du.

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Li, Q., Du, G. Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations. Numer Algor 88, 1915–1936 (2021). https://doi.org/10.1007/s11075-021-01100-1

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