We illustrate how some interesting new variational principles can beused for the numerical approximation of solutions to certain (possiblydegenerate) parabolic partial differential equations. One remarkablefeature of the algorithms presented here is that derivatives do notenter into the variational principles, so, for example, discontinuousapproximations may be used for approximating the heat equation. Wepresent formulae for computing a Wasserstein metric which entersinto the variational formulations.
