Analysis of an Energy-Dissipating Finite Volume Scheme on Admissible Mesh for the Aggregation-Diffusion Equations

We develop the numerical analysis of an energy-dissipating finite volume scheme on admissible meshes for the non-local, nonlinear aggregation-diffusion equations. Crucially, this scheme keeps the dissipation property unconditionally of an associated fully discrete energy, and preserves the mass and positivity conservation of the density. We establish the well-posedness, stability and error analysis of the method. Several numerical examples are presented to verify the theoretical results.