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A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier–Stokes equations

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Abstract

In this report, we present and study a fully discrete finite element variational multiscale scheme for the unsteady incompressible Navier–Stokes equations where high Reynolds numbers are allowed. The scheme uses conforming finite element pairs for spatial discretization and a three-point difference formula for temporal discretization which is of second-order, where a stabilization term based on two local Gauss integrations is employed to stabilize the numerical scheme. We prove stability of the scheme, derive a priori error estimates for the fully discrete solution, and finally, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed numerical scheme.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, People’s Republic of China

    Jufeng Xue & Yueqiang Shang

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  1. Jufeng Xue
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  2. Yueqiang Shang
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Correspondence to Yueqiang Shang.

Additional information

This work was supported by the Natural Science Foundation of China (No. 11361016) and the Basic and Frontier Research Program of Chongqing Municipality, China (No. cstc2016jcyjA0348).

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Xue, J., Shang, Y. A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier–Stokes equations. J. Appl. Math. Comput. 58, 95–110 (2018). https://doi.org/10.1007/s12190-017-1135-y

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  • DOI: https://doi.org/10.1007/s12190-017-1135-y

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