Convergence of approximation schemes for nonlocal front propagation equations

Aurélien Monteillet (1)

1 LM-Brest - Laboratoire de Mathématiques

We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a Fitzhugh-Nagumo type system.

Mots clés: Fitzhugh-Nagumo system; Approximation schemes; front propagations; level-set approach; nonlocal Hamilton-Jacobi equations; second-order equations; viscosity solutions; L^1 dependence in time; dislocation dynamics; Fitzhugh-Nagumo system.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Aurélien Monteillet. Convergence of approximation schemes for nonlocal front propagation equations. 2007. ⟨hal-00326624⟩