LEVEL SET METHODS

    Level Set Methods, introduced by Stanley Osher and James Sethian, are powerful techniques for analyzing and computing moving fronts in a variety of different settings. Level Sets are used in image processing, computer vision, computational fluid dynamics, material science, and many other fields. For a good introduction to Level Set Methods, one may read "Level Set Methods and Dynamic Implicit Surfaces" by Stanley Osher and Ronald Fedkiw.
    There is a variety of methods that numerically approximate level set equations. A few 2D movies below illustrate that third generation methods, HJ ENO and HJ WENO, give much more accurate approximations than first generation schemes, such as Lax-Friedrichs, do.