  Recent advances enable the simultaneous computation of both attracting and
repelling families of Lagrangian Coherent Structures (LCS) at the same initial
or final time of interest. Obtaining LCS positions at intermediate times,
however, has been problematic, because either the repelling or the attracting
family is unstable with respect to numerical advection in a given time
direction. Here we develop a new approach to compute arbitrary positions of
hyperbolic LCS in a numerically robust fashion. Our approach only involves the
advection of attracting material surfaces, thereby providing accurate LCS
tracking at low computational cost. We illustrate the advantages of this
approach on a simple model and on a turbulent velocity data set.
