Numerische Mathematik

, Volume 99, Issue 2, pp 365–379

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

Article

## Summary.

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.

## Keywords

Grid Point Finite Difference Mathematical Method Difference Scheme Centered Difference
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