  In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the
gradient flow of the exterior Bernoulli free boundary problem. We prove here
that the associated energy is non decreasing along the flow. This justifies the
"gradient flow" approach for such kind of problem. The proof relies on the
construction of a discrete gradient flow in the flavour of Almgren-Taylor-Wang
(1993) and on proving it converges to the viscosity solution.
