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Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

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Abstract

A unified analysis is presented for the stabilized methods including the pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations. The existence and uniqueness of the solution and the optimal error estimates are proved.

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References

  1. Bochev, P. B., Dohrmann, C. R., and Gunzburger, M. D. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM Journal on Numerical Analysis, 44, 82–101 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhu, L., Li, J., and Chen, Z. A new local stabilized nonconforming finite element method for solving stationary Navier-Stokes equations. Journal of Computational and Applied Mathematics, 235(8), 2821–2831 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Huang, P. and Chen, J. A stabilized method of P1 nonconforming quadrilateral finite element for solving Stokes problem. Mathematica Numerica Sinica, 32(1), 81–96 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Chen, G. and Feng, M. A new absolutely stable simplified Galerkin Least-Squares finite element method using nonconforming element for the Stokes problem. Applied Mathematics and Computation, 219, 5356–5366 (2013)

    Article  MathSciNet  Google Scholar 

  5. Brezzi, F. and Fortin, M. A minimal stabilization procedure for mixed finite element methods. Numerische Mathematik, 89(3), 457–491 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Burman, E. Pressure projection stabilizations for Galerkin approximations of Stokes’ and Darcy’s problem. Numerical Methods for Partial Differential Equations, 24(1), 127–143 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Matthies, G., Skrzypacz, P., and Tobiska, L. A unified convergence analysis for local projection stabilisations applied to the Oseen problem. Mathematical Modelling and Numerical Analysis, 41, 713–742 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ganesan, S., Matthies, G., and Tobiska, L. Local projection stabilization of equal order interpolation applied to the Stokes problem. Mathematics of Computation, 77, 2039–2060 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhou, T. and Feng, M. A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations. Mathematics of Computation, 60, 531–543 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Park, C. and Sheen, D. P 1-nonconforming quadrilateral finite element methods for second-order elliptic problems. SIAM Journal on Numerical Analysis, 41, 624–640 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. John, V., Maubach, J. M., and Tobiska, L. Nonconforming streamline-diffusion finite element methods for convection-diffusion problems. Numerische Mathematik, 78(2), 165–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Stenberg, R. Analysis of mixed finite element methods for the Stokes problem: a unified approach. Mathematics of Computation, 42, 9–23 (1984)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    Gang Chen  (陈 刚) & Min-fu Feng  (冯民富)

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, P. R. China

    Yin-nian He  (何银年)

Authors
  1. Gang Chen  (陈 刚)
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  2. Min-fu Feng  (冯民富)
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  3. Yin-nian He  (何银年)
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Corresponding author

Correspondence to Min-fu Feng  (冯民富).

Additional information

Project supported by the NationalNatural Science Foundation of China (Nos. 11271273 and 11271298)

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Chen, G., Feng, Mf. & He, Yn. Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations. Appl. Math. Mech.-Engl. Ed. 34, 953–970 (2013). https://doi.org/10.1007/s10483-013-1720-9

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  • DOI: https://doi.org/10.1007/s10483-013-1720-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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