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A convergent scheme for a non-local coupled system modelling dislocations densities dynamics
Author(s):
A.
El Hajj;
N.
Forcadel.
Journal:
Math. Comp.
77
(2008),
789-812.
MSC (2000):
Primary 35Q72, 49L25, 35F25, 35L40, 65M06, 65M12, 65M15, 74H20, 74H25
Posted:
November 8, 2007
MathSciNet review:
2373180
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Additional information
Abstract:
In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence and uniqueness result for the solution of this model. We also propose a convergent numerical scheme and we prove a Crandall-Lions type error estimate between the continuous solution and the numerical one. As far as we know, this is the first error estimate of Crandall-Lions type for Hamilton-Jacobi systems. We also provide some numerical simulations.
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Additional Information:
A.
El Hajj
Affiliation:
Cermics, Ecole des Ponts, ParisTech 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2
N.
Forcadel
Affiliation:
Cermics, Ecole des Ponts, ParisTech 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2
DOI:
10.1090/S0025-5718-07-02038-8
PII:
S 0025-5718(07)02038-8
Keywords:
Hamilton Jacobi equations,
viscosity solutions,
dislocations densities dynamics,
numerical scheme,
error estimate,
system.
Received by editor(s):
June 15, 2006
Received by editor(s) in revised form:
January 26, 2007
Posted:
November 8, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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