Discontinuous Galerkin methods for weakly coupled hyperbolic multi-domain problems

Qingyuan Liu Chi-Wang Shu Brown University Mengping Zhang

Numerical Analysis and Scientific Computing mathscidoc:1804.25011

SIAM Journal on Scientific Computing, 39, A2201-A2230, 2017
In this paper, we develop and analyze the Runge-Kutta discontinuous Galerkin (RKDG) method to solve weakly coupled hyperbolic multi-domain problems. Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains, calling for special techniques to prove stability of the RKDG methods. We prove both stability and error estimates for our RKDG methods on simple models, and then apply them to a biological cell proliferation model \cite{EMSC}. Numerical results are provided to illustrate the good behavior of our RKDG methods.
RKDG scheme, multi-domain problems, discontinuous fluxes, biological cell proliferation model
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@inproceedings{qingyuan2017discontinuous,
  title={Discontinuous Galerkin methods for weakly coupled hyperbolic multi-domain problems},
  author={Qingyuan Liu, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416094803087416046},
  booktitle={SIAM Journal on Scientific Computing},
  volume={39},
  pages={A2201-A2230},
  year={2017},
}
Qingyuan Liu, Chi-Wang Shu, and Mengping Zhang. Discontinuous Galerkin methods for weakly coupled hyperbolic multi-domain problems. 2017. Vol. 39. In SIAM Journal on Scientific Computing. pp.A2201-A2230. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416094803087416046.
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