Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

doi:10.1007/s42967-025-00486-2

Abstract

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.

Key words: Wasserstein gradient flow, Positivity preserving, Energy stability, Porous media equation (PME)

CLC Number:

Shiheng Zhang, Jie Shen. Structure Preserving Schemes for a Class of Wasserstein Gradient Flows[J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 1174-1194.

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