Numerische Mathematik

, Volume 75, Issue 1, pp 17–41

Convergent difference schemes for nonlinear parabolic equations and mean curvature motion

  • Michael G. Crandall
  • Pierre-Louis Lions

DOI: 10.1007/s002110050228

Cite this article as:
Crandall, M. & Lions, P. Numer. Math. (1996) 75: 17. doi:10.1007/s002110050228

Summary.

Explicit finite difference schemes are given for a collection of parabolic equations which may have all of the following complex features: degeneracy, quasilinearity, full nonlinearity, and singularities. In particular, the equation of “motion by mean curvature” is included. The schemes are monotone and consistent, so that convergence is guaranteed by the general theory of approximation of viscosity solutions of fully nonlinear problems. In addition, an intriguing new type of nonlocal problem is analyzed which is related to the schemes, and another very different sort of approximation is presented as well.

Mathematics Subject Classification (1991): 35A40, 35K55, 65M06, 65M12

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michael G. Crandall
    • 1
  • Pierre-Louis Lions
    • 2
  1. 1.Department of Mathematics, University of California, Santa Barbara, CA 93106, USAUS
  2. 2.Ceremade, Université Paris-Dauphine, Place de Lattre de Tassigny, F-75775 Paris 16, FranceFR