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Zbl 1149.65071
Liu, Hai-liang
On discreteness of the Hopf equation. (English)
[J] Acta Math. Appl. Sin., Engl. Ser. 24, No. 3, 423-440 (2008). ISSN 0168-9673; ISSN 1618-3932/e

Summary: The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete equation more accurate than the original equation. These model equations can either be conveniently discretized for producing novel numerical schemes or further analyzed to enrich the theory of nonlinear partial differential equations.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35L65 Conservation laws

Keywords: Hopf equation; dispersive scheme; shock capturing schemes; multi-valued solutions; level set equation; Goudman-Lax scheme; centered scheme; hyperbolic conservation laws

Cited in: Zbl 1206.35221 Zbl 1218.35175

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