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

Cyril Imbert (1) , Marwa Koumaiha (2, 1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

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 one hand, we prove the convergence of the numerical solution towards the weak (viscosity) solution of the Hamilton-Jacobi equation as the mesh size tends to zero for general junction conditions. On the other hand, we derive error estimates of order (∆x) 1 3 in L ∞ loc for junction conditions of optimal-control type.

Mots clés: Hamilton-Jacobi equations; junction conditions; viscosity solutions; flux-limited solutions; error estimates; vertex test function

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Marwa Koumaiha. Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction. 2015. ⟨hal-01120210v1⟩