标题： 非局部守恒律有限体积逼近的精度分析 显示英文标题

标题： On the accuracy of the finite volume approximations to nonlocal conservation laws

摘要： 本文讨论了一类单调有限体积格式逼近非局部标量守恒律的误差分析，这些守恒律用于建模交通流和人群动力学，且假设核函数 $\mu$ 和通量 $f$ 不具有任何额外的单调性或线性假设。 我们首先针对这类偏微分方程证明了一个新的Kuznetsov型引理，并由此表明有限体积近似以速率 $\sqrt{\Delta t}$ 收敛到熵解，收敛发生在 $L^1(\mathbb{R})$ 上。 据我们所知，这是此类守恒律收敛率证明的首次成果。我们还给出了数值实验来说明这一结果。 显示英文摘要

摘要： In this article, we discuss the error analysis for a certain class of monotone finite volume schemes approximating nonlocal scalar conservation laws, modeling traffic flow and crowd dynamics, without any additional assumptions on monotonicity or linearity of the kernel $\mu$ or the flux $f$. We first prove a novel Kuznetsov-type lemma for this class of PDEs and thereby show that the finite volume approximations converge to the entropy solution at the rate of $\sqrt{\Delta t}$ in $L^1(\mathbb{R})$. To the best of our knowledge, this is the first proof of any type of convergence rate for this class of conservation laws. We also present numerical experiments to illustrate this result.