论文标题
双曲线保护法的数值解决方案的后验错误估计
A posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws
论文作者
论文摘要
该论文涉及一类数值方案的后验错误范围，以一个空间维度为$ n \ times n $双曲保护定律。这些估计值是通过“后处理算法”来实现的，可以检查数值解决方案是否保留了较小的总变化，并计算其对合适子域的振荡。该结果特别适用于戈多诺夫或lax炸式方案获得的解决方案，向后的欧拉近似以及周期性平滑的方法。提出了一些数值实现。
The 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.
