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Convergence of approximation schemes for nonlocal front propagation equations

Author: Aurélien Monteillet
Journal: Math. Comp. 79 (2010), 125-146
MSC (2000): Primary 65M12, 53C44, 35K65, 70H20, 49L25
Published electronically: June 8, 2009
MathSciNet review: 2552220
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Abstract: We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of a weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a FitzHugh-Nagumo type system.

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Additional Information

Aurélien Monteillet
Affiliation: Université de Bretagne Occidentale, UFR Sciences et Techniques, 6 av. Le Gorgeu, BP 809, 29285 Brest, France

Keywords: Approximation schemes, front propagations, level-set approach, nonlocal Hamilton-Jacobi equations, second-order equations, viscosity solutions, $L^1$ dependence in time, dislocation dynamics, FitzHugh-Nagumo system.
Received by editor(s): September 22, 2008
Received by editor(s) in revised form: February 13, 2009
Published electronically: June 8, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.