A posteriori error estimates for the effective Hamiltonian of dislocation dynamics

被引：6
作者：
Cacace, S. [2 ]
Chambolle, A. [3 ]
Monneau, R. [1 ]
机构：
[1] CERMICS, Ecole Natl Ponts & Chaussees, F-77455 Champs Sur Marne 2, Marne La Vallee, France
[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[3] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau, France
来源：
NUMERISCHE MATHEMATIK | 2012年 / 121卷 / 02期
关键词：
NONLOCAL EIKONAL EQUATION; JACOBI EQUATIONS; CONVERGENT SCHEME; NUMERICAL-METHODS; HOMOGENIZATION; APPROXIMATION; UNIQUENESS; EXISTENCE; FRONTS;
D O I：
10.1007/s00211-011-0430-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：281 / 335
页数：55
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