论文标题
梯度流的高阶，半幅图，能量稳定方案
High order, semi-implicit, energy stable schemes for gradient flows
论文作者
论文摘要
我们在进化方程的一般环境中引入了一类高阶准确的，半幅度的runge-kutta方案，这些方程是成本函数的梯度流，这可能是关于取决于解决方案的内部产品的梯度流，我们建立了他们的能量稳定性。该类包括特殊情况高阶，通过凸出分裂获得的无条件稳定方案。新方案在各种梯度流中进行了证明，包括相对于Wasserstein（Mass Transper）距离的梯度流量的部分微分方程。
We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the solution, and we establish their energy stability. This class includes as a special case high order, unconditionally stable schemes obtained via convexity splitting. The new schemes are demonstrated on a variety of gradient flows, including partial differential equations that are gradient flow with respect to the Wasserstein (mass transport) distance.
