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arXiv · 2007.13572

High order, semi-implicit, energy stable schemes for gradient flows

Alexander Zaitzeff·Selim Esedoglu·Krishna Garikipati
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Abstract

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.

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Alexander Zaitzeff, Selim Esedoglu, Krishna Garikipati. 2020-07-24. High order, semi-implicit, energy stable schemes for gradient flows. https://doi.org/10.1016/j.jcp.2021.110688

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