Homogenisation of one-dimensional discrete optimal transport

P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal Des Mathematiques Pures et Appliquees (n.d.).


Journal Article | In Press | English
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Abstract
This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport.
Publishing Year
Date Published
2020-02-19
Journal Title
Journal des Mathematiques Pures et Appliquees
ISSN
IST-REx-ID

Cite this

Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. Journal des Mathematiques Pures et Appliquees. doi:10.1016/j.matpur.2020.02.008
Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (n.d.). Homogenisation of one-dimensional discrete optimal transport. Journal Des Mathematiques Pures et Appliquees. https://doi.org/10.1016/j.matpur.2020.02.008
Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal Des Mathematiques Pures et Appliquees, n.d. https://doi.org/10.1016/j.matpur.2020.02.008.
P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” Journal des Mathematiques Pures et Appliquees.
Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. Journal des Mathematiques Pures et Appliquees.
Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal Des Mathematiques Pures et Appliquees, Elsevier, doi:10.1016/j.matpur.2020.02.008.

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