New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third order consistent, energy stable schemes, which are then demonstrated on several partial differential equations that arise as gradient flow with respect to the 2-Wasserstein metric.

翻译：针对作为度量梯度流的演化方程，本文提出了多步法、多阶段法和混合法的能量稳定性新准则。这些准则被用于构造二阶和三阶一致的能量稳定格式，并随后在多个作为2-Wasserstein度量梯度流的偏微分方程上进行了验证。