Journal
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
Volume 24, Issue 3, Pages 423-440Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10255-008-8021-1
Keywords
Hopf equation; dispersive scheme; shock capturing schemes; multi-valued solutions; level set equation
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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.
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