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arXiv · 2607.28195

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

Marco Di Francesco
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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.

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Marco Di Francesco. 2026-07-30. The Follow-the-Leader scheme with non-monotone velocity. https://arxiv.org/abs/2607.28195

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