A convergent scheme for a non local Hamilton Jacobi equation modelling dislocation dynamics

Numerische Mathematik

Volumn 104, Issue 4, 2006, Pages 413-444

  Alvarez, O ^a   Carlini, E ^b   Monneau, R ^c   Rouy, E ^d  

^a UNIVERSITÉ DE ROUEN   (France)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c UNIVERSITÉ PARIS EST   (France)

^d ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749241699     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-006-0030-5     Document Type: Article

References (13)

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2. Alvarez, O., Carlini, E., Monneau, R., Rouy, E.: Convergence of a first order scheme for a non local eikonal equation. IMACS J. Appl. Numer. Math. 56, 1136-1146 (2006)
3. Alvarez, O., Hoch, P., Le Bouar, Y., Monneau, R.: Existence et unicité en temps court d'une solution de viscosité discontinue d'une équation de Hamilton-Jacobi non locale décrivant la dynamique d'une dislocation. Note C.R. Acad. Sci. Paris, Ser. I 338, 679-684 (2004)
4. Alvarez, O., Hoch, P., Le Bouar, Y., Monneau, R.: Dislocation dynamics driven by the self-force: short time existence and uniqueness of the solution. Arch. Rational Mech. Anal. 181(3), 449-504 (2006)
5. Barles, G.: Solutions de Viscosité des Equations de Hamilton-Jacobi. Springer, Berlin Heidelberg New York (1994)
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7. Crandall, M.G., Lions, P.-L.: On existence and uniqueness of solutions of Hamilton-Jacobi equations. Nonlin. Anal. 10, 353-370 (1986)
8. Crandall, G., Evans, L.C., Lions, P.L.: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 282, 487-502 (1984)
9. Hirsh, J.P., Lothe, J.: Theory of Dislocations, 2nd Edn. Krieger, Malabar, FL (1992)
10. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi. J. Comput. Phys. 79, 12-49 (1988)
11. Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867-84 (1992)
12. Sabac, F.: The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws. SIAM J. Numer. Anal. 34(6), 2306-2318 (1997)
13. Xiang, Y., Cheng, L.T., Srolovitz, D.J., Asserman, W.E.: A level set method for dislocation dynamics. Acta Mater. 51(18), 5499-5518 (2003)