On discreteness of the Hopf equation


DOI: 10.1007/s10255-008-8021-1

Cite this article as:
Liu, H. Acta Math. Appl. Sin. Engl. Ser. (2008) 24: 423. doi:10.1007/s10255-008-8021-1


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.


Hopf equation dispersive scheme shock capturing schemes multi-valued solutions level set equation 

2000 MR Subject Classification

65M06 35L65 

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Iowa State UniversityIowaUSA

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