  The good mesh quality of an evolving discretized surface or domain is often
compromised during time evolution. In recent years this phenomena have been
overcome in a couple of ways, one of them uses arbitrary Lagrangian Eulerian
maps. However, the numerical computation of such maps, without a priori
knowledge, still remained elusive. An algorithm is proposed here to numerically
compute an arbitrary Lagrangian Eulerian map, which helps to preserve the mesh
properties over time. The algorithm is based on finding an equilibrium state of
a mechanical system of springs, which is determined by the connectivity of the
nodes in the mesh. We present various numerical experiments illustrating the
good properties of the algorithm.
