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. © 2011 Springer-Verlag.
A posteriori error estimates for the effective Hamiltonian of dislocation dynamics / Cacace, S.; Chambolle, A.; Monneau, R.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 121:2(2012), pp. 281-335. [10.1007/s00211-011-0430-z]
A posteriori error estimates for the effective Hamiltonian of dislocation dynamics
Cacace S.;
2012
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. © 2011 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
