A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD

@article{Deppe2021AHS,
  title={A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD},
  author={Nils Deppe and François H{\'e}bert and Lawrence E. Kidder and Saul A. Teukolsky},
  journal={Classical and Quantum Gravity},
  year={2021},
  volume={39}
}
We present a discontinuous Galerkin (DG)–finite difference (FD) hybrid scheme that allows high-order shock capturing with the DG method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited DG candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust FD methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It… 

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