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Zbl 0736.65066
Osher, Stanley; Shu, Chi-Wang
High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. (English)
[J] SIAM J. Numer. Anal. 28, No.4, 907-922 (1991). ISSN 0036-1429; ISSN 1095-7170/e

The first author and {\it J. A. Sethian} [J. Comput. Phys. 79, No. 1, 12- 49 (1988; Zbl 0659.65132)]\ constructed essentially nonoscillatory (ENO) schemes for the Hamilton-Jacobi equation and its perturbations, arising in front propagation problems.\par In this paper a more general ENO scheme construction procedure is provided mainly by considering different multidimensional monotone building blocks. The schemes are numerically tested on a variety of one- and two-dimensional problems including a problem related to control optimization, checking the accuracy in smooth regions, resolution of discontinuities in derivatives, and the phenomenon of convergence to viscosity solutions.
[V.A.Kostova (Russe)]

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35L45 First order hyperbolic systems, initial value problems

Keywords: essentially nonoscillatory schemes; Hamilton-Jacobi equation; front propagation problems; control optimization; convergence to viscosity solutions

Citations: Zbl 0659.65132

Cited in: Zbl 1202.76127 Zbl 0917.65059

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