## Abstract

We present a spacetime discontinuous Galerkin (SDG) finite element method for scalar hyperbolic conservation laws. The method is consistent with the integral forms of the conservation law and its associated entropy condition written in terms of the physical Godunov flux on each spacetime element. The discrete basis functions are piecewise continuous in spacetime, admitting discontinuities across element boundaries. The resulting Bubnov-Galerkin method is high-order stable for both convex and non-convex flux functions; it does not require stabilization beyond the basic Galerkin projection. The SDG method is applicable to both layered and unstructured spacetime grids. An element-by-element solution scheme delivers O(N) computational complexity (where N is the number of elements) when applied to spacetime meshes that conform to a special causality constraint. We employ two different limiters to control the local overshoot and undershoot that the basic SDG projection generates near shocks.

Original language | English (US) |
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Pages (from-to) | 3607-3631 |

Number of pages | 25 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 193 |

Issue number | 33-35 |

DOIs | |

State | Published - Aug 20 2004 |

## Keywords

- Conservation laws
- Discontinuous Galerkin
- Finite element method
- Godunov flux
- Spacetime

## ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications