High order, semi-implicit, energy stable schemes for gradient flows
High order, semi-implicit, energy stable schemes for gradient flows
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DOI：
10.1016/j.jcp.2021.110688
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Alexander Zaitzeff;S. Esedoglu;K. Garikipati
中科院分区：
文献类型：
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作者：
Alexander Zaitzeff;S. Esedoglu;K. Garikipati
我们引入一类高阶精确，半隐式龙格-库塔格式的一般设置的演化方程，出现作为梯度流的成本函数，可能相对于一个内部产品，取决于解决方案，我们建立他们的能量稳定性。这一类包括作为一个特殊情况下，高阶，无条件稳定的计划，通过凸分裂。各种梯度流，包括偏微分方程，是梯度流相对于Wasserstein（质量运输）距离的新方案证明。
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.