  A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow,
is numerically solved in one space dimension using a higher-order minimizing
movement scheme based on the BDF (backward differentiation formula)
discretization. In each time step, the approximation is obtained as the
solution of a constrained quadratic minimization problem on a
finite-dimensional space consisting of piecewise quadratic basis functions. The
numerical scheme conserves the mass and dissipates the $G$-norm of the two-step
BDF time approximation. Numerically, also the discrete entropy and variance are
decaying. The decay turns out to be exponential in all cases. The corresponding
decay rates are computed numerically for various grid numbers.
