标题： 守恒律半离散逼近的收敛率 显示英文标题

标题： Convergence rate for a semidiscrete approximation of scalar conservation laws

摘要： 我们提出了一种半离散格式，用于逼近一维数量守恒律在非负初值条件下的熵解。 该格式基于守恒律的粒子路径概念，可以被解释为有限粒子离散化。证明了收敛率与初始粒子间距有关，为$1/2$阶。 作为一个特例，这涵盖了 Follow-the-Leader 模型收敛到交通流的 Lighthill-Whitham-Richards 模型的结果。 显示英文摘要

摘要： We propose a semidiscrete scheme for approximation of entropy solutions of one-dimensional scalar conservation laws with nonnegative initial data. The scheme is based on the concept of particle paths for conservation laws and can be interpreted as a finite-particle discretization. A convergence rate of order $1/2$ with respect to initial particle spacing is proved. As a special case, this covers the convergence of the Follow--the--Leader model to the Lighthill--Whitham--Richards model for traffic flow.