| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 761 - 784 | |
| DOI | https://doi.org/10.1051/m2an/2026020 | |
| Published online | 09 April 2026 | |
Convergence rate for a semidiscrete approximation of scalar conservation laws
Department of Mathematics, University of Oslo, Oslo, Norway
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
22
July
2025
Accepted:
17
February
2026
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.
Mathematics Subject Classification: 65M12 / 35L65 / 90B20
Key words: Scalar conservation laws / particle paths / traffic flow
© The authors. Published by EDP Sciences, SMAI 2026
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