This paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for \(n\times n\) hyperbolic conservation laws in one space dimension. These estimates are achieved by a “post-processing algorithm”, checking that the numerical solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, in particular, to solutions obtained by the Godunov or the Lax–Friedrichs scheme, backward Euler approximations, and the method of periodic smoothing. Some numerical implementations are presented.

中文翻译：

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双曲守恒律数值解的后验误差估计

对于一维空间上的（n \ times \ n）双曲守恒律，本文涉及一类广泛的数值格式的后验误差界。这些估计是通过“后处理算法”实现的，检查数值解是否保留了较小的总变化，并在适当的子域上计算其振荡。结果特别适用于通过Godunov或Lax-Friedrichs方案，反向Euler逼近以及周期平滑方法获得的解。介绍了一些数值实现。