Convergence of a first order scheme for a non-local Eikonal equation

Authors:
O. Alvarez;E. Carlini;R. Monneau;E. Rouy
Affiliations:
Université de Rouen, Mont-Saint Aignan cedex, France;Dipartimento di Matematica, Università di Roma "La Sapienza", Rome, Italy;CERMICS, Citè Descartes - Champs sur Marne, Marne la Vallèe cedex, France;Departement de Mathematiques, Ecole Centrale de Lyon, Ecully cedex, France
Venue:
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Year:
2006

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Abstract

We prove the convergence of a first order finite difference scheme approximating a non-local eikonal Hamilton-Jacobi equation. The non-local character of the problem makes the scheme not monotone in general. However, by using in a convenient manner the convergence result for monotone scheme of Crandall-Lions, we obtain the same bound √|ΔX|+Δt for the rate of convergence.