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

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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.

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  1. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Adam M. Oberman

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  1. Adam M. Oberman
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Correspondence to Adam M. Oberman.

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Mathematics Subject Classification (2000): 35K65, 35K55, 65M06, 65M12

The author would like to thank P.E. Souganidis for valuable discussions, and the University of Texas at Austin for its hospitality during the course of this work.

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Oberman, A. A convergent monotone difference scheme for motion of level sets by mean curvature. Numer. Math. 99, 365–379 (2004). https://doi.org/10.1007/s00211-004-0566-1

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  • DOI: https://doi.org/10.1007/s00211-004-0566-1

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