Skip to main content
SpringerLink
Log in

Mass- and Momentum Conservation of the Least-Squares Spectral Element Method for the Stokes Problem

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

The opinion that least-squares methods are not useful due to their poor mass conserving property should be revised. It will be shown that least-squares spectral element methods perform poorly with respect to mass conservation, but this is compensated with a superior momentum conservation. With these new insights, one can firmly state that the least-squares spectral element method remains an interesting alternative for the commonly used Galerkin spectral element formulation

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernardi C., and Maday Y. (1992). Approximations Spectrale de Problèmes aux Limites Élliptiques. Springer-Verlag, Paris

    Google Scholar 

  2. Chang C.L., and Nelson J.J. (1997). Least-squares finite element method for the Stokes problem with zero residual of mass conservation. SIAM J. Numer. Anal 34(2):480–489

    Article  MathSciNet  Google Scholar 

  3. Deang J.M., and Gunzburger M.D. (1998). Issues related to least-squares finite element methods for the Stokes equations. SIAM J. Sci. Comput 20(3):878–906

    Article  MathSciNet  Google Scholar 

  4. Deville M.O., Fischer P.F., and Mund E.H. (2002). High-Order Methods for Incompressible Fluid Flow. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge

    Google Scholar 

  5. Gerritsma M.I., and Proot M.M.J. (2002). Analysis of a discontinuous least squares spectral element method. J. Sci. Comput 17(1–3):323–333

    Article  Google Scholar 

  6. Karniadakis G.E., and Sherwin S.J. (1999). Spectral/hp Element Methods for CFD. Oxford University Press, Oxford

    Google Scholar 

  7. Maday Y., and Patera A.T. (1989). Spectral element methods for the incompressible Navier-Stokes equations. In: Noor A. K., and Oden J.T (eds). State-of-the-Art Surveys in Computational Mechanics. ASME, NY

    Google Scholar 

  8. Nool, M., and Proot, M. M. J. (2002). Parallel implementation of a least-squares spectral element solver for incompressible flow problems. In International Conference on Computational Science, Amsterdam, The Netherlands, April 21–24. Springer

  9. Nool, M., and Proot, M. M. J. (2002). A parallel state-of-the-art least-squares spectral element solver for incompressible flow problems. In VECPAR 2002 Conference on High Performance Computing for Computational Science, Porto, Portugal, June 26–28. Universidade do Porto, Faculdade de Engenharia

  10. Pontaza J.P., and Reddy J.N. (2003). Spectral/hp least squares finite element formulation for the Navier-Stokes equation. J. Comput. Phys 190(2):523–549

    Article  MathSciNet  ADS  Google Scholar 

  11. Pontaza J.P., and Reddy J.N. (2004). Space-time coupled spectral/hp least squares finite element formulation for the incompressible Navier-Stokes equation. J. Comput. Phys 197(2):418–459

    Article  ADS  MathSciNet  Google Scholar 

  12. Proot M.M.J. (2003). The Least-Squares Spectral Element Method. Theory, Implementation and Application to Incompressible Flows. Ph.D thesis, Delft University of Technology

  13. Proot M.M.J., and Gerritsma M.I. (2002). A least-squares spectral element formulation for the Stokes problem. J. Sci. Comput 17(1–3):311–322

    Article  Google Scholar 

  14. Proot M.M.J., and Gerritsma M.I. (2002). Least-squares spectral elements applied to the Stokes problem. J. Comput. Phys 181(2):454–477

    Article  CAS  ADS  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. Michael M. J. Proot

    Present address: Shell Global Solutions International B.V., The Hague, The Netherlands

Authors and Affiliations

  1. Aerospace Engineering, Aerodynamics Section, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands

    Michael M. J. Proot

  2. Aerospace Engineering, Aerodynamics Section, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands

    Marc I. Gerritsma

Authors
  1. Michael M. J. Proot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marc I. Gerritsma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael M. J. Proot.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Proot, M.M.J., Gerritsma, M.I. Mass- and Momentum Conservation of the Least-Squares Spectral Element Method for the Stokes Problem. J Sci Comput 27, 389–401 (2006). https://doi.org/10.1007/s10915-005-9030-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-005-9030-3

Keywords

Search

Navigation