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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A numerical analysis of upwind type schemes for the nonlinear nonlocalaggregation equation is provided. In this approach, the aggregation equation isinterpreted as a conservative transport equation driven by a nonlocal nonlinearvelocity field with low regularity. In particular, we allow the interactingpotential to be pointy, in which case the velocity field may havediscontinuities. Based on recent results of existence and uniqueness of aFilippov flow for this type of equations, we study an upwind finite volumenumerical scheme and we prove that it is convergent at order 1/2 in Wassersteindistance. This result is illustrated by numerical simulations, which show theoptimality of the order of convergence.

Convergence analysis of upwind type schemes for the aggregation equation with pointy potential