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Some results on uniformly high-order accurate essentially nonoscillatory schemes
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
1986 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 2, no 3-5, 347-377 p.Article in journal (Refereed) Published
Abstract [en]

We continue the construction and the analysis of essentially nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy in the sense of truncation error, at extrema of the solution. In this paper we construct an hierarchy of uniformly high-order accurate approximations of any desired order of accuracy which are tailored to be essentially nonoscillatory. This means that, for piecewise smooth solutions, the variation of the numerical approximation is bounded by that of the true solution up to O(hR - 1), for 0 <R and h sufficiently small. The design involves an essentially nonoscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. To solve this reconstruction problem we use a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities.

Place, publisher, year, edition, pages
1986. Vol. 2, no 3-5, 347-377 p.
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-90511DOI: 10.1016/0168-9274(86)90039-5,OAI: diva2:505752
NR 20140805Available from: 2012-02-24 Created: 2012-02-24Bibliographically approved

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Engquist, Björn
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