Abstract
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.
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© 1986 Springer-Verlag New York Inc.
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Harten, A. (1986). On High-Order Accurate Interpolation for Non-Oscillatory Shock Capturing Schemes. In: Dafermos, C., Ericksen, J.L., Kinderlehrer, D., Slemrod, M. (eds) Oscillation Theory, Computation, and Methods of Compensated Compactness. The IMA Volumes in Mathematics and Its Applications, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8689-6_4
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DOI: https://doi.org/10.1007/978-1-4613-8689-6_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8691-9
Online ISBN: 978-1-4613-8689-6
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