We prove the convergence of an approximation scheme for computing evolutions having various normal velocities depending on the curvature. This scheme is an extension of the Bence-Merriman-Osher scheme for computing mean curvature motions. To obtain the convergence, we make use of the new weak notion of fronts motion introduced by G. Barles and P.E. Souganidis, which is equivalent, under the no -interior condition, to the well-known level set evolution.
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