We study the problem of time–step adaptation in semi–Lagrangian schemes for the approximation of the level–set equation of Mean Curvature Motion. We try to present general principles for time adaptivity strategies applied to geometric equations and to make a first attempt based on local truncation error. The efficiency of the proposed technique on classical benchmarks is discussed in the last section.
Carlini, E., Falcone, M., Ferretti, R. (2006). A time-adaptive Semi-Lagrangian approximation to Mean Curvature Motion. In Numerical Mathematics and Advanced Applications - ENUMATH 2005 (pp.732-739). BERLIN : Springer [10.1007/978-3-540-34288-5_71].