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Two-grid stabilized methods for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions

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  • Qiu, Hailong

Abstract

In this paper, we consider a two-grid quadratic equal-order stabilized method for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions. Our two-grid stabilized method consists of computing one nonlinear problem on a coarse mesh and then solving a linearization correction problem on a fine mesh. Moreover, the stability and convergence of the present method are derived. Finally, numerical experiments are performed to confirm our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:172-188
    DOI: 10.1016/j.amc.2018.03.066
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    Cited by:

    1. 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).
    2. Pei, Lifang & Zhang, Chaofeng & Shi, Dongyang, 2024. "Unconditional superconvergence analysis of two-grid nonconforming FEMs for the fourth order nonlinear extend Fisher-Kolmogorov equation," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    3. 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).

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