A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)433-454
Journal / PublicationArchive for Rational Mechanics and Analysis
Issue number2
Publication statusPublished - May 2010


In this paper, we introduce a new Glimm functional for general systems of hyperbolic conservation laws. This new functional is consistent with the classical Glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate, so that it can be viewed as "optimal" in some sense. With this new functional, the consistency of the Glimm scheme is proved clearly for general systems. Moreover, the convergence rate of the Glimm scheme is shown to be the same as the one obtained in Bressan, Marson (Arch Ration Mech Anal 142(2):155-176, 1998) for systems with each characteristic field being genuinely nonlinear or linearly degenerate. © Springer-Verlag 2009.