Skip to main content

A-Priori Estimates for a Semi-Lagrangian Scheme for the Wave Equation

  • Chapter
Godunov Methods
  • 1353 Accesses

Abstract

We present some a-priori estimates for a class of semi-Lagran-gian approximation schemes for the wave equation. The wave equation is written in the form of a hyperbolic system of the first order and the approximation is based on this representation. The algorithm can work on structured and unstructured grids.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Crandall M.G., Ishii H. and Lions P.L. (1992). User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc.27 , pp.1–67.

    Article  MathSciNet  Google Scholar 

  • Falcone M. and Ferretti R. (1994). Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations. Numer. Math.67, pp. 315–344.

    Article  MathSciNet  Google Scholar 

  • Falcone M. and Ferretti R. (1998). Convergence analysis for a class of semi-lagrangian advecion schemes. SIAM J. Num. Anal.35, pp. 909–940.

    Article  Google Scholar 

  • Falcone M. and Ferretti R. (2000). Analysis of a class of semi-Lagrangian schemes for the wave equation. In preparation.

    MATH  Google Scholar 

  • Harten A., Osher S., Engquist B. and Chakravarthy S. (1986). Some results on uniformly high-order accurate essentially non-oscillatory schemes. Appl. Nurner. Math.2, pp. 347–377.

    MATH  Google Scholar 

  • Hoar R.H. and Vogel C.R. (1995). An adaptive stencil finite differencing scheme for linear first order hyperbolic systems - a preliminary report. Computation and control, IV (Bozeman, MT, 1994), 169–183, Progr. Systems Control Theory, 20, Birkhäuser Boston, Boston, MA, 1995.

    MATH  Google Scholar 

  • Barles G. (1994). Solutions de viscosité des equations de Hamilton-Jacobi. Springer-Verlag, Paris.

    MATH  Google Scholar 

  • Quarteroni A. and Valli A. (1994). Numerical approximation of partial differential equations. Springer-Verlag.

    Book  Google Scholar 

  • Whitham .B. (1974). Linear and non linear waves. Wiley-Interscience, New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Falcone, M., Ferretti, R. (2001). A-Priori Estimates for a Semi-Lagrangian Scheme for the Wave Equation. In: Toro, E.F. (eds) Godunov Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-0663-8_30

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-0663-8_30

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-5183-2

  • Online ISBN: 978-1-4615-0663-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics