A convergent entropy-dissipating BDF2 finite-volume scheme for a population cross-diffusion system
Numerical Analysis
2023-01-10 v1 Numerical Analysis
Abstract
A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the mass. The existence and uniqueness of discrete solutions and their large-time behavior as well as the convergence of the scheme are proved. The proofs are based on the G-stability of the BDF2 scheme, which provides an inequality for the quadratic Rao entropy and hence suitable a priori estimates. The novelty is the extension of this inequality to the system case. Some numerical experiments in one and two space dimensions underline the theoretical results.
Keywords
Cite
@article{arxiv.2301.03200,
title = {A convergent entropy-dissipating BDF2 finite-volume scheme for a population cross-diffusion system},
author = {Ansgar Jüngel and Martin Vetter},
journal= {arXiv preprint arXiv:2301.03200},
year = {2023}
}