Skip to main content
SpringerLink
Log in

Spectral methods for the computation of discontinuous solutions

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The extension of spectral methods to the computation of discontinuous weak solutions of hyperbolic equations is considered. A new postprocessing method that produces a close to spectral accuracy is introduced. Conservation of moments with spectral accuracy is proved for the linear case. Model problems demonstrate the theoretical results. Numerical results are also included.

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

  • Courant, R., and Hubert, D. (1953).Methods of Mathematical Physics, Interscience, New York, Vol. 2.

    Google Scholar 

  • Davis, P. J., and Rabinowitz, P. (1967).Numerical Integration. Blaisdell, Waltham, Massachusetts.

    Google Scholar 

  • Gottlieb, D., and Turkel, E. Spectral methods for time dependent partial differential equations, Contract Nos. NAS1-16394 and NAS1-17130.

  • Gottlieb, D., and Orszag, S. A. (1977). Numerical analysis of spectral methods theory and applications, CBMS Regional Conference Series 26, SIAM.

  • Hussaini, M. Y., Kopriva, D. A., Salas, M. D., and Zang, T. A. (1983). Spectral methods for the Euler equations, Proc. of the 6th AIAA Computational Fluid Dynamics Conference Danvers, Massachusetts.

  • Lax, P. D. (1978). Accuracy and resolution in the computation of solutions of linear and nonlinear equations.Recent Adv. Num. Anal. Proc. Symp., Mathematical Research Center, University of Wisconsin, Academic Press, New York.

    Google Scholar 

  • Lin, C. C., Yuan, C., and Shu, F. H. (1969). On the spiral structure of disk galaxies III: Comparison with observations,Astrophys. J. 155.

  • Majda, A., McDonough, J., and Osher, S. (1978). The Fourier method for nonsmooth initial data,Math. Comput. 32.

  • Mock, M. S., and Lax, P. D. (1978). The computation of discontinuous solutions of linear hyperbolic equations,Comm. Pure Appl. Math. 31.

  • Orszag, S. A., and Patterson, D. S. (1972). Numerical simulation of three dimensional homogeneous isotropic turbulence,Phys. Rev. Lett. 28.

  • Orszag, S. A. (1980). Spectral methods for problems in complex geometries,J. Comput. Phys. 37.

  • Roberts, W. W. (1969). Large-scale shock formation in spiral galaxies and its implications on star formation,Astrophys. J. 158.

  • Schmidt, M. (1965).Galactic Structure, University of Chicago Press, Chicago.

    Google Scholar 

  • Shu, F. H.et al. (1972). Galactic shock in an interstellar medium with two stable phases,Astrophys. J. 173.

  • Woodward, P. R. (1975). On the nonlinear time development of gas flow in spiral density waves,Astrophys. J. 195.

Download references

Authors
  1. Nira Gruberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gruberger, N. Spectral methods for the computation of discontinuous solutions. J Sci Comput 4, 71–117 (1989). https://doi.org/10.1007/BF01061267

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01061267

Keywords

Search

Navigation