2023/01/09 by Jüngel, Ansgar, Vetter, Martin
#35Q92 #65L06 #65M08 #65M12 #92D25 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2301.03200
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.