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- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Appl.Mathematics/Computational Methods of Engineering
- ISSN
- 0029-599X
- eISSN
- 0945-3245
- DOI
- 10.1007/s00211-004-0566-1
- Publisher site
- See Article on Publisher Site
Abstract
An explicit convergent finite difference scheme for motion of level sets by mean curvature is presented. The scheme is defined on a cartesian grid, using neighbors arranged approximately in a circle. The accuracy of the scheme, which depends on the radius of the circle, dx, and on the angular resolution, d θ, is formally O(dx 2+d θ). The scheme is explicit and nonlinear: the update involves computing the median of the values at the neighboring grid points. Numerical results suggest that despite the low accuracy, acceptable results are achieved for small stencil sizes. A numerical example is presented which shows that the centered difference scheme is non-convergent.
Journal
Numerische Mathematik – Springer Journals
Published: Nov 5, 2004