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1 CMAP - Centre de Mathématiques Appliquées 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Abstract : We study an implicit and discontinuous scheme for a non-local Hamilton-Jacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall-Lions type for the error between continuous and discrete solutions. We deduce an a posteriori error estimate for the effective Hamiltonian associated to a stationary cell problem. In dimension one and under suitable assumptions, we also give improved a posteriori estimates. Numerical simulations are provided.

Keywords : dislocation dynamics Hamilton-Jacobi implicit scheme a posteriori error estimate effective Hamiltonian viscosity solutions





Autor: Simone Cacace - Antonin Chambolle - Régis Monneau -

Fuente: https://hal.archives-ouvertes.fr/



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