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.

在本文中，我们讨论了一类单调有限体积方案的误差分析，该方案逼近非局部标量守恒定律，对交通流和人群动态进行建模，而无需对内核 \(\mu \) 或通量 f.我们首先证明了此类偏微分方程的一个新颖的库兹涅佐夫型引理，从而表明有限体积近似以 \(\sqrt{\Delta t}\) 的速率收敛到熵解，其中 \(L^1(\) mathbb {R})\)。据我们所知，这是此类守恒定律任何类型收敛率的第一个证明。我们还提出了数值实验来说明这一结果。