# Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction

Abstract : This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau (2013) to general junction conditions. On the one hand, we prove the convergence of the numerical solution towards the viscosity solution of the Hamilton-Jacobi equation as the mesh size tends to zero for general junction conditions. On the other hand, we derive optimal error estimates of order $(\Delta x)^{\frac{1}{2}}$ in $L_{loc}^{\infty}$ for junction conditions of optimal-control type at least if the flux is "strictly limited".
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Type de document :
Pré-publication, Document de travail
39 pages. In the initial version, the proof of the error estimate only works for Hamiltonians wit.. 2017

https://hal.archives-ouvertes.fr/hal-01120210
Contributeur : Jessica Guerand <>
Soumis le : vendredi 2 juin 2017 - 17:14:31
Dernière modification le : mardi 24 avril 2018 - 17:20:06
Document(s) archivé(s) le : mercredi 13 décembre 2017 - 02:41:59

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• HAL Id : hal-01120210, version 2
• ARXIV : 1502.07158

### Citation

Jessica Guerand, Marwa Koumaiha. Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction. 39 pages. In the initial version, the proof of the error estimate only works for Hamiltonians wit.. 2017. 〈hal-01120210v2〉

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