## Abstract

In this work we introduce and analize a new explicit method for solving numerically scalar conservation laws. The time-discretization of the method is based on a second order accurate TVD Runge-Kutta technique (used recently by Osher and Shu to solve scalar conservation laws in the framework of finite difference schemes), while the space-discretization is based on a discontinuous finite element method for which the approximate solution is taken to be piecewise linear in space (i. e., the local projection P^{0}P^{1} -discontinuous Galerkin method introduced recently by Chavent and Cockbum). The resulting scheme is TVBM (total variation bounded in the means), converges to a weak solution, and is formally second order accurate in time and space for cfl ε [0, 1/3]. We give extensive numerical evidence that the scheme does converge to the entropy solution, and that the order of convergence away from singularities is optimal; i. e., equal to 2 in the norm of L^{∞}(L^{∞}_{loc}).

Original language | English (US) |
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State | Published - Jan 1 1988 |

Event | 1st National Fluid Dynamics Conference, 1988 - Cincinnati, United States Duration: Jul 25 1988 → Jul 28 1988 |

### Other

Other | 1st National Fluid Dynamics Conference, 1988 |
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Country/Territory | United States |

City | Cincinnati |

Period | 7/25/88 → 7/28/88 |