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A three-step stabilized algorithm for the Navier-Stokes type variational inequality

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  • Zheng, Bo
  • Shang, Yueqiang

Abstract

In the light of two-grid finite element discretization, this paper is concerned with a three-step stabilized algorithm for the Navier-Stokes equations with nonlinear slip boundary conditions of friction type. The proposed algorithm proceeds three steps: the first step solves a stabilized nonlinear variational inequality problem on a coarse grid, the second step solves a stabilized linear variational inequality problem based on Newton iteration on a fine grid, and the third step solves the same stabilized linear problem with only different right-hand sides on a fine grid. We analyze the stability of the presented algorithm, and derive error estimate of the approximate solutions in L2 norms of the velocity gradient and pressure. Finally, we demonstrate the effectiveness of the present algorithm by two numerical tests.

Suggested Citation

  • Zheng, Bo & Shang, Yueqiang, 2022. "A three-step stabilized algorithm for the Navier-Stokes type variational inequality," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005379
    DOI: 10.1016/j.amc.2022.127463
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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.
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