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We study an implicit finite-volume scheme for non-linear, non-localaggregation-diffusion equations which exhibit a gradient-flow structure,recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this schemekeeps the dissipation property of an associated fully discrete energy, and doesso unconditionally with respect to the time step. Our main contribution in thiswork is to show the convergence of the method under suitable assumptions on thediffusion functions and potentials involved.

Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations