  Curves of maximal slope are a reference gradient-evolution notion in metric
spaces and arise as variational formulation of a vast class of nonlinear
diffusion equations. Existence theories for curves of maximal slope are often
based on minimizing-movements schemes, most notably on the Euler scheme. We
present here an alternative minimizing-movements approach, yielding more
regular discretizations, serving as a-posteriori convergence estimator, and
allowing for a simple convergence proof.
