Convergence rate for a semidiscrete approximation of scalar conservation laws

Fuente: arXiv
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Autor principal: Ørke, Magnus C.
Formato: Preprint
Publicado: 2025
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author Ørke, Magnus C.
author_facet Ørke, Magnus C.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_10951
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Convergence rate for a semidiscrete approximation of scalar conservation laws
Ørke, Magnus C.
Analysis of PDEs
Numerical Analysis
65M12, 35L65, 90B20
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.
title Convergence rate for a semidiscrete approximation of scalar conservation laws
topic Analysis of PDEs
Numerical Analysis
65M12, 35L65, 90B20
url https://arxiv.org/abs/2504.10951