  ESFEM is a method introduced in order to solve a linear advection-diffusion
equation on an evolving two-dimensional surface with finite elements by using a
moving grid with nodes sitting on and evolving with the surface. The evolution
of the surface is assumed to be given as a smooth one-parameter family of
embeddings of a fixed initial surface into $\mathbb{R}^3$ satisfying uniform
$C^4$ bounds. We calculate an equivalent transformed equation which is defined
on the fixed initial surface and can hence be solved numerically on a fixed
grid. We present numerical examples which indicate that both approaches are
essentially of the same accuracy.
