Skip to main content

A fractional step method for regularized Navier-Stokes equations

Numerical Methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 1530)

Keywords

  • Scalar Multiplication
  • Discretization Error
  • Finite Element Approximation
  • Orthogonality Relation
  • Stokes Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, R.A.: Sobolev Spaces. New York et al., Academic Press 1975

    MATH  Google Scholar 

  2. Cattabriga, L.: Su un Problema al Contorno Relativo al Sistema di Equazioni di Stokes. Sem. Mat. Univ. Padova 31 (1964) 308–340

    MathSciNet  MATH  Google Scholar 

  3. Girault, V., Raviart, P.A.: Finite Element Approximation of the Navier-Stokes Equations. Berlin et al., Springer 1979

    CrossRef  MATH  Google Scholar 

  4. Heywood, J.G., Rannacher, R.: Finite Element Approximation of the Nonstationary Navier-Stokes Problem. II. Stability of Solutions and Error Estimates Uniform in Time. Siam J. Numer. Anal. 23 (1986) 750–777

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  5. Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951) 213–231

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Kaniel, S., Shinbrot, M.: The Initial Value Problem for the Navier-Stokes Equations. Arch. Rat. Anal. 21 (1966) 270–285

    MathSciNet  MATH  Google Scholar 

  7. Lax, P.D., Richtmeyer, R.D.: Survey of the Stability of Linear Finite Difference Equations. Com. Pure Appl. Math. 9 (1956) 267–293

    CrossRef  MathSciNet  Google Scholar 

  8. Rautmann, R.: Zur Konvergenz des Rothe-Verfahrens für instationäre Stokes-Probleme in dreidimensionalen Gebieten. Z. Angew. Math. Mech. (ZAMM) 64 (1984) T387–T388

    MathSciNet  MATH  Google Scholar 

  9. Temam, R.: Navier-Stokes Equations. Amsterdam et al., North Holland 1977

    MATH  Google Scholar 

  10. Varnhorn, W.: Zur Numerik der Gleichungen von Navier-Stokes. Universität Paderborn, Dissertation 1985

    MATH  Google Scholar 

  11. Varnhorn, W.: Time Stepping Procedures for the Nonstationary Stokes Equations. Preprint 1353 Technische Hochschule Darmstadt (1991) 1–20 (to appear in Math. Meth. Appl. Sci)

    Google Scholar 

  12. Varnhorn, W.: Time Delay and Finite Differences for the Nonstationary Nonlinear Navier-Stokes Equations. Preprint 1359 Technische Hochschule Darmstadt (1991) 1–27 (to appear in Math. Meth. Appl. Sci)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Varnhorn, W. (1992). A fractional step method for regularized Navier-Stokes equations. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations II — Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090343

Download citation

  • DOI: https://doi.org/10.1007/BFb0090343

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56261-0

  • Online ISBN: 978-3-540-47498-2

  • eBook Packages: Springer Book Archive