论文标题
Wasserstein梯度流的TPFA有限体积近似
TPFA Finite Volume Approximation of Wasserstein Gradient Flows
论文作者
论文摘要
已经显示出在瓦斯坦斯坦空间中显示出在不同领域出现的许多无限尺寸动力学系统。我们构建了两点通量近似有限体积方案，使这些问题分配了保留变异结构并具有二阶精度的此类问题。我们提出了一种内部方法来解决离散的变分问题，提供了一种有效且可靠的算法。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。
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.
