In this reading seminar, I will discuss the fully discrete finite-volume scheme for the Fokker-Planck equation suggested in [Cancès, C., Monsaingeon, L. and Natale, A., 2024. Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach. arXiv preprint arXiv:2410.03367]. The scheme is designed to be second-order accurate in both time and space and to satisfy a fully discrete counterpart of the energy-dissipation inequality for the Fokker-Planck equation. For the scheme to meet all these properties, in particular, the authors introduce a novel nonlinear midpoint rule for discretization in time. I will explain the scheme construction and present the ideas of the convergence proof based on passing to the limit in the energy-dissipation inequality.