Maximum time step for the BDF3 scheme applied to gradient flows

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

Generalized Maximum Flows over Time

Flows over time and generalized ows are two advanced network ow models of utmost importance, as they incorporate two crucial features occurring in numerous real-life networks. Flows over time feature time as a problem dimension and allow to realistically model the fact that commodities (goods, information, etc.) are routed through a network over time. Generalized ows allow for gain/loss factors...

Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to e...

A JKO Splitting Scheme for Kantorovich-Fisher-Rao Gradient Flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting som...

Finite-time convergent gradient flows with applications to network consensus

This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finite-time convergence. We discuss the application of the results to consensus problems in multiagent systems and show how th...