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.

中文翻译：

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交叉扩散系统的收敛熵递减有限体积方案

我们研究了交叉扩散系统的两点通量近似有限体积方案。该方案被证明保留了连续系统的关键特性，其中包括熵的衰减。由于基于离散熵 - 熵耗散估计的紧凑性，该方案的收敛性得以建立。数值结果说明了我们方案的行为。