The Follow-the-Leader scheme with non-monotone velocity

Marco Di Francesco

The Follow-the-Leader scheme with non-monotone velocity

Analysis of PDEs 2026-07-30 v1

Authors: Marco Di Francesco

Abstract

This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity map is \emph{non monotone}. The result is based on a discrete maximum principle, on $BV$ estimates of the approximated density, and on the characterization of the limit as entropy solution in the sense of Kru\v zkov.

Keywords

scalar conservation law Follow-the-Leader scheme entropy solution non-monotone velocity discrete maximum principle BV estimates

Cite

@article{arxiv.2607.28195,
  title  = {The Follow-the-Leader scheme with non-monotone velocity},
  author = {Marco Di Francesco},
  journal= {arXiv preprint arXiv:2607.28195},
  year   = {2026}
}