Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum
arXiv:2602.01145
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.