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A posteriori error estimates for the effective Hamiltonian of dislocation dynamics |
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| Authors: | S Cacace A Chambolle R Monneau |
| Institution: | 1. Dipartimento di Matematica, Sapienza Universit?? di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy 2. CMAP, Ecole Polytechnique CNRS, Route de Saclay, 91128, Palaiseau Cedex, France 3. CERMICS, Ecole Nationale des Ponts et Chauss??es, 6 et 8 avenue Blaise Pascal, Cit?? Descartes, Champs-sur-Marne, 77455, Marne-la-Vall??e Cedex 2, France |
| Abstract: | We study an implicit and discontinuous scheme for a non-local Hamilton?CJacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall?CLions 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. |
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