We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the notion of geodesic extrapolation in the Wasserstein space, which in general is not uniquely defined. We propose several possible definitions for such an operation, and we prove convergence of the resulting scheme to the limit PDE, in the case of the Fokker-Planck equation. For a specific choice of extrapolation we also prove a more general result, that is convergence towards EVI flows. Finally, we propose a variational finite volume discretization of the scheme which numerically achieves second order accuracy in both space and time.

翻译：我们对瓦西斯坦梯度流采用基于经典的向后偏差公式的瓦西斯坦梯度流采用时间分解法。这个办法的主要基石是瓦西斯坦空间的大地测量外推法概念,一般说来,瓦西斯坦空间的大地测量外推法并不是独特的定义。我们为这种作业提出了若干可能的定义,并且证明,在Fokker-Planck等式中,由此产生的办法与PDE的限度一致。对于外推法的具体选择,我们也证明一个比较普遍的结果,即与EVI流动相融合。最后,我们建议对这个办法进行一个可变的有限量分解法,以数字方式在空间和时间上都达到第二顺序的精确度。