Convergence of a particle method for diffusive gradient flows in one   dimension
  We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the gradient flow structure at the particle level. The strategy of the proof is based on an abstract result for the convergence of curves of maximal slope in metric spaces. 
J. A. Carrillo, F. S. Patacchini, P. Sternberg, G. Wolansky
math.AP