Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations
Numerical Analysis
2022-04-19 v4 Numerical Analysis
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2002.10821,
title = {Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations},
author = {Rafael Bailo and Jose A. Carrillo and Hideki Murakawa and Markus Schmidtchen},
journal= {arXiv preprint arXiv:2002.10821},
year = {2022}
}