## Abstract

Abstract: The accuracy of the discontinuous Galerkin method of the third-order approximation on smooth solutions in the calculation of discontinuous solutions of a quasilinear hyperbolic system of conservation laws with shock waves propagating with a variable velocity is studied. As an example, the approximation of the system of conservation laws of shallow water theory is considered. On the example of this system, it is shown that, like the TVD and WENO schemes of increased order of approximation on smooth solutions, the discontinuous Galerkin method, despite its high accuracy on smooth solutions and in the localization of shock waves, reduces its order of convergence to the first order in the shock wave influence domain.

Original language | English |
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Pages (from-to) | 1344-1353 |

Number of pages | 10 |

Journal | Computational Mathematics and Mathematical Physics |

Volume | 58 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

## Keywords

- discontinuous Galerkin method
- hyperbolic system of conservation laws
- integral and local convergence order
- shallow water theory
- CONVERGENCE
- DIFFERENCE-SCHEMES
- HYPERBOLIC CONSERVATION-LAWS