High order, semi-implicit, energy stable schemes for gradient flows
arXiv:2007.13572 · doi:10.1016/j.jcp.2021.110688
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.
arXiv admin note: text overlap with arXiv:1908.10246