Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws

Xue Luo Beihang University

Numerical Analysis and Scientific Computing mathscidoc:1804.25034

Applied Numerical Mathematics, 123, 256-274, 2018
In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution by using compensated compactness arguments, under some conditions. The numerical experiments of the inviscid Burger's equation support our result, and it verifies the reasonableness of the conditions.
spectral viscosity method, generalized Hermite functions, nonlinear conservation laws, compensated compactness arguments
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@inproceedings{xue2018spectral,
  title={Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws },
  author={Xue Luo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416124623410859069},
  booktitle={Applied Numerical Mathematics},
  volume={123},
  pages={256-274},
  year={2018},
}
Xue Luo. Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws . 2018. Vol. 123. In Applied Numerical Mathematics. pp.256-274. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416124623410859069.
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