Convergence rate for a semidiscrete approximation of scalar conservation laws
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909580078874624 |
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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 |