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

Abstract

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 entropyentropy dissipation estimate. Numerical results illustrate the behavior of our scheme.