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A nonconforming finite element method for the stationary Smagorinsky model

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  • Shi, Dongyang
  • Li, Minghao
  • Li, Zhenzhen

Abstract

In this paper, we focus on a low order nonconforming finite element method (FEM) for the stationary Smagorinsky model. The velocity and pressure are approximated by the constrained nonconforming rotated Q1 element (CN Q1rot) and piecewise constant element, respectively. Optimal error estimates of the velocity in the broken H1-norm and L2-norm, and the pressure in the L2-norm are derived by some nonlinear analysis techniques and Aubin-Nitsche duality argument. The supercloseness and superconvergent results are also obtained under some reasonable regularity assumptions. Finally, a numerical example is implemented to confirm our theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Li, Minghao & Li, Zhenzhen, 2019. "A nonconforming finite element method for the stationary Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 308-319.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:308-319
    DOI: 10.1016/j.amc.2019.02.012
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    References listed on IDEAS

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    1. An, Rong & Li, Yuan & Zhang, Yuqing, 2016. "Error estimates of two-level finite element method for Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 786-800.
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    Cited by:

    1. Zheng, Bo & Shang, Yueqiang, 2022. "A two-step stabilized finite element algorithm for the Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Yuhan Wang & Peiyao Wang & Rongpei Zhang & Jia Liu, 2024. "Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method," Mathematics, MDPI, vol. 12(12), pages 1-11, June.

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    1. Zheng, Bo & Shang, Yueqiang, 2022. "A two-step stabilized finite element algorithm for the Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 422(C).

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