  We define the elastic energy of smooth immersed closed curves in
$\mathbb{R}^n$ as the sum of the length and the $L^2$-norm of the curvature,
with respect to the length measure. We prove that the $L^2$-gradient flow of
this energy smoothly converges asymptotically to a critical point. One of our
aims was to the present the application of a Lojasiewicz-Simon inequality,
which is at the core of the proof, in a quite concise and versatile way.
