Skip to main content

A Two-Level Stabilized Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations

  • Conference paper
Book cover High Performance Computing and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5938))

  • 2312 Accesses

Abstract

In this paper, we combine a stabilized nonconforming finite element method with a two-level method to solve the stationary Navier-Stokes equations. Numerical results are presented to show the convergence performance of this combined algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, Z.: Finite Element Methods and Their Applications. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  2. Douglas Jr., J., Santos, J.E., Sheen, D., Ye, X.: Nonconforming Galenkin methods based on quadrilateral elements for second order elliptic problems. Math. Modelling and Numerical Analysis 33, 747–770 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cai, Z., Douglas Jr., J., Ye, X.: A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations. Calcolo (36), 215–232 (1999)

    Google Scholar 

  4. Kim, Y., Lee, S.: Stable nonconforming quadrilateral finite elements for the Stokes problem. Applied Mathematics and Computation 115, 101–112 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Li, J., Chen, Z.: A new local stabilized nonconforming finite element method for the Stokes equations. Computing (82), 157–170 (2008)

    Google Scholar 

  6. Zhu, L., Li, J., Chen, Z.: A new local stabilized nonconforming fintite element method for the stationary Navier-Stokes equations (submitted for publication)

    Google Scholar 

  7. Xu, J.: A novel two-grid method for semilinear elliptic equatios. SIAM J. Sci. Comput. 15, 231–237 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. Xu, J.: Two-grid finite element discritizations for nonlinear PDEs. SIAM J. Numer. Anal. 33, 1759–1777 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Layton, W.: A two-level discretization method for the Navier-Stokes equations. Comput. Math. Appl. 26, 33–38 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  10. Layton, W., Lenferink, W.: Two-level Picard and modified Picard methods for the Navier-Stokes equatios. Appl. Math. Comput. 69, 263–274 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Layton, W., Tobiska, L.: A two-level method with backtracking for the Navier-Stokes equations. SIAM J. Numer. Anal. 35, 2035–2054 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Girault, V., Lions, J.L.: Two-grid finite element scheme for the transient Navier-Stokes problem. Math. Model. and Numer. Anal. 35, 945–980 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. He, Y., Li, J., Yang, X.: Two-level penalized finite element methods for the stationary Navier-Stokes equations. Intern. J. Inform. System Sciences 2, 1–16 (2006)

    MathSciNet  Google Scholar 

  14. Olshanskii, M.A.: Two-level method and some a priori estimates in unsteady Navier-Stokes calculations. J. Comp. Appl. Math. 104, 173–191 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. He, Y.: Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. 41, 1263–1285 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. He, Y.: A two-level finite Element Galerkin method for the nonstationary Navier-Stokes Equations, I: Spatial discretization. J. Comput. Math. 22, 21–32 (2004)

    MATH  MathSciNet  Google Scholar 

  17. He, Y., Miao, H., Ren, C.: A two-level finite Element Galerkin method for the nonstationary Navier-Stokes equations, II: Time discretization. J. Comput. Math. 22, 33–54 (2004)

    MATH  MathSciNet  Google Scholar 

  18. He, Y., Liu, K.M.: Multi-level spectral Galerkin method for the Navier-Stokes equations I: time discretization. Adv in Comp. Math. 25, 403–433 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. He, Y., Liu, K.M., Sun, W.W.: Multi-level spectral Galerkin method for the Navier-Stokes equations I: Spatial discretization. Numer. Math. 101, 501–522 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhu, L., Chen, Z. (2010). A Two-Level Stabilized Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_81

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11842-5_81

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11841-8

  • Online ISBN: 978-3-642-11842-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics