On the numerical approximation of one-dimensional nonconservative hyperbolic systems

@article{Chalmers2013OnTN,
  title={On the numerical approximation of one-dimensional nonconservative hyperbolic systems},
  author={N. Chalmers and Emmanuel Lorin},
  journal={J. Comput. Science},
  year={2013},
  volume={4},
  pages={111-124}
}
Attempts to define weak solutions to nonconservative hyperbolic systems have lead to the development of several approaches, most notably the path-based theory of Dal Maso, LeFloch, and Murat (DLM) and the vanishing viscosity solutions described by Bianchini and Bressan. While these theories enable us to define weak solutions to nonconservative hyperbolic systems, difficulties arise when numerically approximating these systems. Specifically, in the neighborhood of a discontinuity, the numerical… CONTINUE READING

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