Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such problems which preserve the variational structure and have second order accuracy in space. We propose an interior point method to solve the discrete variational problem, providing an efficient and robust algorithm. We present two applications to test the scheme and show its order of convergence.

中文翻译：

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Wasserstein 梯度流的 TPFA 有限体积近似

在不同领域出现的许多无限维动力系统已被证明在 Wasserstein 空间中表现出梯度流结构。我们构建了两点通量逼近有限体积方案，将此类问题离散化，保留变分结构并在空间中具有二阶精度。我们提出了一种解决离散变分问题的内点方法，提供了一种有效且鲁棒的算法。我们提出了两个应用程序来测试该方案并显示其收敛顺序。