A mixed finite element discretization of dynamical optimal transport

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

In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by Papadakis et al. [SIAM J Imaging Sci, 7(1):212–238,2014]. We solve the discrete problem using a proximal-splitting approach and we show how to modify this in the presence of regularization terms which are relevant for imaging applications.

Domaines: Analyse numérique [math.NA]

Andrea Natale, Gabriele Todeschi. A mixed finite element discretization of dynamical optimal transport. 2020. ⟨hal-02501634v3⟩