Second order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

Guillaume Legendre (1) , Gabriel Turinici (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IUF - Institut universitaire de France

The time discretization of gradient flows in metric spaces uses variants of the celebrated implicit Euler-type scheme of Jordan, Kinderlehrer and Otto. We propose in this Note a different approach which allows to construct two second order in time numerical schemes. We show that these schemes are well defined and prove (theoretically and numerically) the convergence for a gradient flow in the Wasserstein space corresponding to a Fokker–Planck equation.

Domaines: Analyse numérique [math.NA]

Guillaume Legendre, Gabriel Turinici. Second order in time schemes for gradient flows in Wasserstein and geodesic metric spaces. 2016. ⟨hal-01317769v1⟩