A convergent entropy diminishing finite volume scheme for a cross-diffusion system

01/30/2020
by   Clément Cancès, et al.
0

We study a two-point flux approximation finite volume scheme for a cross-diffusion system. The scheme is shown to preserve the key properties of the continuous systems, among which the decay of the entropy. The convergence of the scheme is established thanks to compactness properties based on the discrete entropy - entropy dissipation estimate. Numerical results illustrate the behavior of our scheme.

READ FULL TEXT

page 20

page 21

research
07/05/2022

Study of a structure preserving finite volume scheme for a nonlocal cross-diffusion system

In this paper we analyse a finite volume scheme for a nonlocal version o...
research
07/20/2020

Finite volumes for the Stefan-Maxwell cross-diffusion system

The aim of this work is to propose a provably convergent finite volume s...
research
05/04/2020

Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

We study a time implicit Finite Volume scheme for degenerate Cahn-Hillia...
research
03/28/2023

Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface

We propose a two-point flux approximation finite-volume scheme for the a...
research
04/03/2023

Convergence of a finite volume scheme and dissipative measure-valued-strong stability for a hyperbolic-parabolic cross-diffusion system

This article is concerned with the approximation of hyperbolic-parabolic...
research
06/10/2022

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations

We study a finite volume scheme for the approximation of the solution to...
research
02/28/2022

Using the Dafermos Entropy Rate Criterion in Numerical Schemes

The following work concerns the construction of an entropy dissipative f...

Please sign up or login with your details

Forgot password? Click here to reset