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

Journal of Mathematical Analysis and Applications 2026 Open access

Read full text
Authors: M. Di Francesco, Simone Fagioli, Valeria Iorio, Massimiliano D. Rosini
DOI: 10.1016/j.jmaa.2026.131108
Cited by: 0

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.

Fields of Study & Subjects

Computational Fluid Dynamics and Aerodynamics Differential Equations and Numerical Methods Advanced Numerical Methods in Computational Mathematics

Publication details

Journal / source
Journal of Mathematical Analysis and Applications
Volume
567
Issue
2
Pages
131108–131108
Publication date
29 September 2026
Language
EN