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A two-level stabilized quadratic equal-order finite element variational multiscale method for incompressible flows

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  • Zheng, Bo
  • Shang, Yueqiang

Abstract

A two-level stabilized quadratic equal-order variational multiscale method based on the finite element discretization is proposed for numerically solving the steady incompressible Navier-Stokes equations at high Reynolds numbers. In this method, a stabilized solution is first obtained by solving a fully stabilized nonlinear system on a coarse grid, and then the solution is corrected by solving a stabilized linear problem on a fine grid. Under the condition of N∥f∥H−1(Ω)ν(ν+α)<1, the stability of the present method is analyzed, and error estimates of the approximate solutions from the proposed method are deduced. The effectiveness of the proposed method is demonstrated by some numerical results.

Suggested Citation

  • Zheng, Bo & Shang, Yueqiang, 2020. "A two-level stabilized quadratic equal-order finite element variational multiscale method for incompressible flows," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    • Handle: RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320303374
    DOI: 10.1016/j.amc.2020.125373
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    References listed on IDEAS

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    1. Qiu, Hailong, 2018. "Two-grid stabilized methods for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 172-188.
    2. Zheng, Bo & Shang, Yueqiang, 2019. "Parallel iterative stabilized finite element algorithms based on the lowest equal-order elements for the stationary Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 35-56.
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