TPFA Finite Volume Approximation of Wasserstein Gradient Flows

Andrea Natale (1) , Gabriele Todeschi (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such problems which preserve the variational structure and have second order accuracy in space. We propose an interior point method to solve the discrete variational problem, providing an efficient and robust algorithm. We present two applications to test the scheme and show its order of convergence.

Mots clés: Wasserstein gradient flows; Energy diminishing scheme

Domaines: Analyse numérique [math.NA]

Andrea Natale, Gabriele Todeschi. TPFA Finite Volume Approximation of Wasserstein Gradient Flows. Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02444833v2⟩