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

Jiale Hua Zaihong Jiang Tong Yang

Analysis of PDEs mathscidoc:1912.43974

Archive for rational mechanics and analysis, 196, (2), 433-454, 2010.5
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):155176, 1998) for systems with each characteristic field being genuinely nonlinear or linearly degenerate.
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@inproceedings{jiale2010a,
  title={A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws},
  author={Jiale Hua, Zaihong Jiang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211012712991538},
  booktitle={Archive for rational mechanics and analysis},
  volume={196},
  number={2},
  pages={433-454},
  year={2010},
}
Jiale Hua, Zaihong Jiang, and Tong Yang. A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws. 2010. Vol. 196. In Archive for rational mechanics and analysis. pp.433-454. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211012712991538.
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