Skip to main content
SpringerLink
Log in
Book cover

Hyperbolic Problems: Theory, Numerics, Applications pp 187–196Cite as

Birkhäuser

Convergence of the Godunov Scheme for Straight Line Systems

  • Conference paper

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 140))

Abstract

Consider the Cauchy problem for an n×n system of the form

$$ {u_t} + A(u){u_x} = 0, u(x,0) = \bar u(x). $$
(1)

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

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
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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. M. Arora, P. L. RoeOn postshock oscillations due to shock capturing schemes in unsteady flowsJ. Comput. Phys.130(1997), 25–40.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. BianchiniOn a Glimm type functional for a special Jin-Xin relaxation modelAnn. Inst. Henri Poincaré - Nonlinear Analysis, to appear.

    Google Scholar 

  3. S. Bianchini, A. BressanBV solutions for a class of viscous hyperbolic systemsIndiana Univ. Math. J.49(2000).

    Google Scholar 

  4. A. BressanThe unique limit of the Glimm schemeArch. Rational Mech. Anal.130(1995), 205–230.

    MathSciNet  MATH  Google Scholar 

  5. A. BressanHyperbolic Systems of Conservation Laws. The One Dimensional Cauchy ProblemOxford University Press, 2000.

    MATH  Google Scholar 

  6. A. Bressan, R. M. ColomboThe semigroup generated by2 x 2conservation lawsArch. Rational Mech. Anal.133(1995), 1–75.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Bressan, G. Crasta, B. PiccoliWell posedness of the Cauchy problem for n x n systems of conservation lawsAmer. Math. Soc. Memoir694(2000).

    Google Scholar 

  8. A. Bressan, T. P. Liu, T. Yang, L1 stability estimates for n x n conservation lawsArch. Rational Mech. Anal.149(1999), 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Bressan, H. K. JenssenOn the convergence of Godunov scheme for nonlinear hyperbolic systemsChinese Ann. Math.21(2000), 1–16.

    Article  MathSciNet  Google Scholar 

  10. A. Bressan, W. ShenBV estimates for multicomponent chromatography with relaxationDiscrete Cont. Dyn. Syst.6(2000), 21–38.

    MathSciNet  MATH  Google Scholar 

  11. R. J. DiPernaConvergence of approximate solutions to conservation lawsArch. Rational Mech. Anal.82(1983), 27–70.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. GlimmSolutions in the Large for Nonlinear Hyperbolic Systems of EquationsComm. Pure. Appl. Math.18(1965), 697–715.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Goodman, Z. XinViscous limits for piecewise smooth solutions to systems of conservation lawsArch. Rational Mech. Anal.121(1992), 235–265.

    MathSciNet  MATH  Google Scholar 

  14. D. KrönerNumerical Schemes for Conservation LawsWiley and Teubner, 1997.

    MATH  Google Scholar 

  15. R. J. LeVeque, B. TempleStability of Godunov’s method for a class of2 x 2systems of conservation lawsSIAM J. Math. Anal.288(1985), 115–123.

    Google Scholar 

  16. D. SerreSolutions with bounded variations for some hyperbolic systems of conservation lawsJ. Differential Equations68(1987), 137–168.

    Article  MathSciNet  MATH  Google Scholar 

  17. S. H. YuZero dissipation limit to solutions with shocks for systems of hyperbolic conservation lawsArch. Rational Mech. Anal.146(1999), 275–370.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S.I.S.S.A., Via Beirut 4, Trieste, 34014, Italy

    Alberto Bressan

  2. Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN, 47405, USA

    Helge Kristian Jenssen

Authors
  1. Alberto Bressan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Helge Kristian Jenssen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, Leipzig, 04103, Germany

    Heinrich Freistühler

  2. Otto-von-Guericke-University, Institute of Analysis and Numerical Mathematics, PSF 4120, Magdeburg, 39106, Germany

    Gerald Warnecke

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Bressan, A., Jenssen, H.K. (2001). Convergence of the Godunov Scheme for Straight Line Systems. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8370-2_20

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9537-8

  • Online ISBN: 978-3-0348-8370-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation