841 research outputs found
A Monotone, Second Order Accurate Scheme for Curvature Motion
We present a second order accurate in time numerical scheme for curve
shortening flow in the plane that is unconditionally monotone. It is a variant
of threshold dynamics, a class of algorithms in the spirit of the level set
method that represent interfaces implicitly. The novelty is monotonicity: it is
possible to preserve the comparison principle of the exact evolution while
achieving second order in time consistency. As a consequence of monotonicity,
convergence to the viscosity solution of curve shortening is ensured by
existing theory
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