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

Abstract

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

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Cited by in corpus (6)

• Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation
• Variational convergence of the Scharfetter-Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit
• On a Class of Nonlocal Continuity Equations on Graphs
• A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
• A nonlocal-to-local approach to aggregation-diffusion equations
• Drift-diffusion equations with saturation