Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system

Abstract

In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and prove its convergence. The proofs rely on a discrete entropy-dissipation inequality, discrete compactness arguments, and on the novel adaptation of the so-called duality method at the discrete level. Finally, thanks to numerical experiments, we investigate the influence of the nonlocality in the system: on convergence properties of the scheme, as an approximation of the local system and on the development of diffusive instabilities.

References in corpus (6)

• A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
• The boundedness-by-entropy principle for cross-diffusion systems
• Spatial memory and taxis-driven pattern formation in model ecosystems
• Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
• Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches
• An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization