On High-Order Accurate Interpolation for Non-Oscillatory Shock Capturing Schemes

  • Ami Harten
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 2)


In this paper we describe high-order accurate Godunov-type schemes for the computation of weak solutions of hyperbolic conservation laws that are essentially non-oscillatory. We show that the problem of designing such schemes reduces to a problem in approximation of functions, namely that of reconstructing a piecewise smooth function from its given cell averages to high order accuracy and without introducing large spurious oscillatons. To solve this reconstruction problem we introduce a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy wherever the function is smooth but avoids having a Gibbs-phenomenon at discontinuities.


Truncation Error Local Extremum Interpolation Technique Entropy Solution Reconstruction Problem 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Ami Harten
    • 1
    • 2
  1. 1.School of Mathematical SciencesTel-Aviv UniversityIsrael
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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