A convergent monotone difference scheme for motion of level sets by mean curvature

Authors:
Adam M. Oberman
Affiliations:
Simon Fraser University, Department of Mathematics, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada
Venue:
Numerische Mathematik
Year:
2004

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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, dθ, is formally O(dx2+dθ). 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.