Modern theory of numerical methods for Motion by Mean Curvature.
Ryo Takei (M.Sc. Thesis), July 2007
Abstract
We analyze two finite difference schemes, the median and the morphological schemes,
for nu-
merically solving the motion by mean curvature partial differential equation.
We show that
these schemes satisfy sufficient conditions for convergence to the correct viscosity
solution
of the underlying equation. Moreover, we explore a recent link between the motion
by mean
curvature partial differential equation to a two-person differential game; we
argue that these
schemes can be interpreted as discrete approximations to this two-person differential
game.
Numerical results comparing the two schemes to standard finite difference discretization
are
also presented.
Keywords:
Motion by mean curvature; Viscosity solutions; Two-person differential games;
Degenerate
elliptic schemes; Finite difference method.
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