Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature
Yoko Goto, Katsuyuki Ishii, Taichi Ogawa · Communications on Pure & Applied Analysis · 2005
A new proof of the convergence of the Bence-Merriman-Osher algorithm for the motion of mean curvature is given. The idea is making use of the approximate distance function to the interface and analogous argument in the singular limiting problem for the Allen-Cahn equation via an auxiliary function given by the primitive function of the heat kernel.