Work

Finite elements for Wasserstein 𝕎p gradient flows

Year: 2025

Type: article

Abstract: Wasserstein 𝕎p gradient flows for nonlinear integral functionals of the density yield degenerate parabolic equations involving diffusion operators of q-Laplacian type, with q being p’s conjugate exponent. We propose a finite element scheme building on conformal 𝕡1 Lagrange elements with mass lumping and a backward Euler time discretization strategy. Our scheme preserves mass and positivity while energy decays in time. Building on the theory of gradient flows in metric spaces, we further prove convergence towards a weak solution of the PDE that satisfies the energy dissipation equality. The analytical results are illustrated by numerical simulations.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025035

Authors: Clément Cancès, Daniel Matthes, Flore Nabet, Eva-Maria Rott

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: Agence Nationale de la Recherche

Awards: G3257718068, Centre Européen pour les Mathématiques, la Physique et leurs Interactions