Convergence rate for a semidiscrete approximation of scalar conservation laws
Abstract
We propose a semidiscrete scheme for approximation of entropy solutions of one-dimensional scalar conservation laws with nonnegative initial data. The scheme is based on the concept of particle paths for conservation laws and can be interpreted as a finite-particle discretization. A convergence rate of order 1/2 with respect to initial particle spacing is proved. As a special case, this covers the convergence of the Follow-the-Leader model to the Lighthill-Whitham-Richards model for traffic flow.
Fields of Study & Subjects
Computational Fluid Dynamics and Aerodynamics
Traffic control and management
Singular Perturbation
Asymptotics and Difference Schemes
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 2
- Pages
- 761–784
- Publication date
- 1 March 2026
- Language
- EN