Abstract In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition.

中文翻译：

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用于标量非线性守恒定律的 Adams-Bashforth 不连续伽辽金方法的先验误差估计

摘要 在本文中，我们展示了二阶 Adams-Bashforth 不连续伽辽金方法的理论收敛性，该方法用于用 E 通量逼近标量非线性守恒定律的平滑解。还为一阶前向欧拉不连续伽辽金方法导出了先验误差估计。速率在时间上是最优的，在空间上是次优的；它们在 CFL 条件下有效。