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A stabilized finite volume method for the stationary Navier–Stokes equations

Author

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  • Sheng, Ying
  • Zhang, Tie
  • Jiang, Zhong-Zhong

Abstract

In the present paper, we propose a stabilized finite volume element method for the Navier–Stokes equations using the lowest order P1−P0 element pair. The stabilized method is designed by adding a jump term of the discrete pressure to the continuity approximation equation. A discrete inf–sup condition is established for the stabilized finite volume element scheme which assures the stability of the discrete solutions. The optimal error estimates are derived in the H1-norm for velocity and the L2-norm for pressure, respectively. Moreover, the optimal L2- error estimate is also given for velocity approximation.

Suggested Citation

  • Sheng, Ying & Zhang, Tie & Jiang, Zhong-Zhong, 2016. "A stabilized finite volume method for the stationary Navier–Stokes equations," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 363-372.
  • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:363-372
    DOI: 10.1016/j.chaos.2016.01.002
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    Cited by:

    1. Bai, Feng & Wang, Yi, 2022. "A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 100-132.
    2. Xiaoling Tang & Aifeng Zhai & Xiaowen Ding & Qiande Zhu, 2019. "Safety Guarantee System of Drinking Water Source in Three Gorges Reservoir Area and Its Application in Huangjuedu Drinking Water Source Area," Sustainability, MDPI, vol. 11(24), pages 1-13, December.

    More about this item

    Keywords

    Finite volume method; Navier–Stokes problem; Stabilized method; P1 − P0 element pair; Inf–sup condition;
    All these keywords.

    JEL classification:

    • P1 - Political Economy and Comparative Economic Systems - - Capitalist Economies
    • P0 - Political Economy and Comparative Economic Systems - - General

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