English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we discuss the error analysis for a certain class ofmonotone finite volume schemes approximating nonlocal scalar conservation laws,modeling traffic flow and crowd dynamics, without any additional assumptions onmonotonicity or linearity of the kernel $\mu$ or the flux $f$. We first prove anovel Kuznetsov-type lemma for this class of PDEs and thereby show that thefinite 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 isthe first proof of any type of convergence rate for this class of conservationlaws. We also present numerical experiments to illustrate this result.

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