Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

Abstract

We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass and positivity and to be uniquely solvable. In addition, they also ensure energy dissipation in many typical scenarios. Through extensive numerical experiments, we demonstrate the schemes’ robustness, accuracy, and efficiency.

Keywords

Wasserstein gradient flow / Positivity preserving / Energy stability / Porous media equation (PME)

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Funding

National Natural Science Foundation of China(12371409)

RIGHTS & PERMISSIONS

Shanghai University