Convergent difference schemes for nonlinear parabolic equations and mean curvature motion

Numerische Mathematik

Volumn 75, Issue 1, 1996, Pages 17-41

  Crandall, Michael G ^a   Lions, Pierre Louis ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030507383     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050228     Document Type: Article

References (22)

1. Barles, G., Souganidis, P.E. (1991): Convergence of approximation schemes for fully nonlinear second-order equations. Asymp. Anal. 4, 271-283
2. Barles, G., Georgelin, A.: A simple procf of convergence for an approximation scheme for computing motions by mean curvature. Preprint
3. Bence, J., Merriman, B., Osher, S. (1994): Motion of multiple junctions - a level set approach. J. Comp. Physics 112, 334-363
4. Catté, F., Dibos, F., Koepfler, G.: Preprint
5. Chen, Y.G., Giga, Y., Goto, S. (1991): Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differ. Geom. 33, 749-786
6. Chen, Y.G., Giga, Y., Hitaka, Y.T., Honma, M. (1994): A stable difference scheme for computing motion of level surfaces by the mean curvature. Proc. Gobal Analysis Research Center Symposium, Seoul, Korea (to appear)
7. Crandall, M.G., Ishii, H., Lions, P.L. (1992), User's guide to viscosity solutions of second order partial differential equations. Bull Amer. Math. Soc. 27, 1-67
8. Crandall, M.G., Lions, P.L. (1984): Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp. 43, 1-19
9. Crandall, M.G., Tartar, L. (1980): Some relations between nonexpansive and order preserving mappings. Proc. Amer. Math. Soc. 78, 385-390
10. Evans, L.C. (1993): Convergence of an algorithm for mean curvature motion. Indiana U. Math. J. 42, 533-557
11. Evans, L.C., Spruck, J. (1991): Motion of level sets by mean curvature, I. J. Differ. Geom. 33. 635-681
12. Guichard, F. (1994): Thesis, University of Paris - Dauphine, Paris
13. Ishii, H. (1984): Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Ind. Univ. Math. J. 33, 721-748
14. Ishii, H.: A generalization of the Bence, Merriman and Osher algorithm for motion by mean curvature. Preprint
15. Kocan, M.: Approximation ov viscosity solutions of elliptic partial differential equations on minimal grids. Preprint
16. Kuo, H.J., Trudinger, N.S. (1990): Linear elliptic difference inequalities with random coefficients. Math. Comp. 55, 37-53
17. Kuo, H.J., Trudinger, N.S. (1992): Discrete methods for fully nonlinear elliptic equations. SIAM J. Numer. Anal. 29, 123-135
18. Kuo, H.J., Trudinger, N.S. (1993): On the discrete maximum principle for parabolic difference operators. RAIRO Math. Model. Num. Anal. 27, 719-737
19. Marshall, A.W., Olkin, I. (1979): Inequalities: theory of majorization and its applications. Mathematics in Science and Engineering 143, Academic Press, New York
20. Motzkin, T.S., Wasow, W. (1952): On the approximation of linear elliptic differential equations by difference equations with positive coefficients. J. Math. Phys. 31, 253-259
21. Osher, S., Sethian, J. (1988): Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 79, 12-49
22. Souganidis, P.E. (1985): Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Differ. Equa. 59, 1-43