DeepAI AI Chat
Log In Sign Up

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

by   Alexander Zaitzeff, et al.

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.


High Order Schemes for Gradient Flow with Respect to a Metric

New criteria for energy stability of multi-step, multi-stage, and mixed ...

Variational Extrapolation of Implicit Schemes for General Gradient Flows

We introduce a class of unconditionally energy stable, high order accura...

A general class of linear unconditionally energy stable schemes for the gradient flows

This paper studies a class of linear unconditionally energy stable schem...

Stable Neural Flows

We introduce a provably stable variant of neural ordinary differential e...

The gradient flow structures of thermo-poro-visco-elastic processes in porous media

In this paper, the inherent gradient flow structures of thermo-poro-visc...

Fast and Stable Schemes for Phase Fields Models

We propose and analyse new stabilized time marching schemes for Phase Fi...

High-order maximum-entropy collocation methods

This paper considers the approximation of partial differential equations...