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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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F. Al Reda and B. Maury

15 Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

F. Al Reda, Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, 91405 Orsay cedex, France

B. Maury, Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, 91405 Orsay cedex, France

Abstract: This paper establishes a link between some space discretization strategies of the finite volume type for the Fokker–Planck equation in general meshes (Voronoï tesselations) and gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein distances on graphs recently proposed by Maas [6].

Keywords: Gradient flows, Wasserstein distance, finite volumes ...

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