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- ItemOn gradient structures for Markov chains and the passage to Wasserstein gradient flows(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Disser, Karoline; Liero, MatthiasWe study the approximation of Wasserstein gradient structures by their finite-dimensional analog. We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible Markov chains. Then we reprove the convergence of the discrete scheme in the limit of vanishing mesh size using only the involved gradient-flow structures. In particular, we make no use of the linearity of the equations nor of the fact that the Fokker-Planck equation is of second order.