Abstract: A new approach is introduced to prove optimal L¹-error estimates for various approximate methods, such as viscosity methods, monotone difference schemes and stiff relaxation approximations, to conservation laws. The new approach is a matching method, which is quite different from the well-known Kuznetsov's approach, an error analysis method for conservation laws. So far the best available L¹-convergent rate, by using Kuznetsov approach, for these popular approximate methods is only half-order, even though these methods are of first-order accuracy to conservation laws. But by using the new approach a first-order rate of L¹-convergence for these methods can be approved, which is an improvement over the half-order rates of L¹-convergence.

Key words: shock waves, conservation laws, error estimates

摘要： 介绍一种误差分析的新途径，并对守恒律方程各种近似方法如粘性法，单调差分格式及松弛近似等证明了最佳L¹误差估计。新途径是一种匹配方法，它不同于著名的Kuznetsov方法。众所周知，上述近似方法具有一阶精度，但Kuznetsov方法给出的最佳L¹收敛速度仅为二分之一阶。应用新途径可以证明上述方法具有一阶收敛性。

关键词: 激波, 守恒律方程, 误差估计