A numerical study for the homogenisation of one-dimensional models describing the motion of dislocations

DOI10.1504/IJCSM.2008.019712zbMath1178.65098OpenAlexW2015299031MaRDI QIDQ1040618

Philippe Hoch, Régis Monneau, Mohamed Ali Ghorbel

Publication date: 25 November 2009

Published in: International Journal of Computing Science and Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1504/ijcsm.2008.019712

zbMATH Keywords

Hamilton-Jacobi equationnumerical examplesfinite difference schemetransport equationeikonal equationeffective HamiltonianPeach-Koehler forcecrystal defectsnumerical homogenisationdislocations dynamicsnon-local equationcontinuous viscosity solutionCourant Friedrichs-Lewy conditionsdislocation defects

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Hamilton-Jacobi equations (35F21)

Related Items (4)

A posteriori error estimates for the effective Hamiltonian of dislocation dynamics ⋮ Percival Lagrangian approach to the Aubry-Mather theory ⋮ Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics ⋮ A Generalized Newton Method for Homogenization of Hamilton--Jacobi Equations

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