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arXiv · 2602.01145

Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum

M. Di Francesco·S. Fagioli·V. Iorio·M. D. Rosini
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Abstract

We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle equations and show that an appropriate piecewise-constant density reconstruction from the particle setting converges to the unique entropy weak solution of the macroscopic scalar conservation law.

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M. Di Francesco, S. Fagioli, V. Iorio, M. D. Rosini. 2026-02-01. Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum. https://arxiv.org/abs/2602.01145

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