守恒律方程误差估计的新途径(英文)

A New Approach to Error Estimates for Conservation Laws 1)

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。

A new approach is introduced to prove optimal L 1 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 L 1 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 L 1 convergence for these methods can be approved,which is an improvement over the half order rates of L 1 convergence.