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A characteristic stabilized finite element method for the non-stationary Navier–Stokes equations

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Abstract

This paper is concerned with the analysis of a new stabilized method based on the local pressure projection. The proposed method has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures. Error estimates of the velocity and the pressure are obtained for both the continuous and the fully discrete versions. Finally, some numerical experiments show that this method is highly efficient for the non-stationary Navier–Stokes equations.

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Authors and Affiliations

  1. The Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Hongen Jia

  2. College of Mathematics and System Science, Xinjiang University, Urmuqi, 830046, China

    Demin Liu

  3. The College of Science, Xi’an Jiaotong University, Xi’an, 710049, China

    Hongen Jia, Demin Liu & Kaitai Li

Authors
  1. Hongen Jia
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  2. Demin Liu
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  3. Kaitai Li
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Correspondence to Hongen Jia.

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Jia, H., Liu, D. & Li, K. A characteristic stabilized finite element method for the non-stationary Navier–Stokes equations. Computing 93, 65–87 (2011). https://doi.org/10.1007/s00607-011-0153-0

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  • DOI: https://doi.org/10.1007/s00607-011-0153-0

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