article published yes Peter Gladbach author Eva Kopfer author Jan Maas author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338 Lorenzo Portinale author 30AD2CBC-F248-11E8-B48F-1D18A9856A87 JaMa department Optimal Transport and Stochastic Dynamics project Taming Complexity in Partial Differential Systems project Dissipation and dispersion in nonlinear partial differential equations project 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. Elsevier2020 eng 0021-7824 1905.05757 00053943940000810.1016/j.matpur.2020.02.008 1397204-234 https://research-explorer.ista.ac.at/record/10030 Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier, 2020. <a href="https://doi.org/10.1016/j.matpur.2020.02.008">https://doi.org/10.1016/j.matpur.2020.02.008</a>. Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier. <a href="https://doi.org/10.1016/j.matpur.2020.02.008">https://doi.org/10.1016/j.matpur.2020.02.008</a> Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7), 204–234. P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7. Elsevier, pp. 204–234, 2020. Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. 2020;139(7):204-234. doi:<a href="https://doi.org/10.1016/j.matpur.2020.02.008">10.1016/j.matpur.2020.02.008</a> Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:<a href="https://doi.org/10.1016/j.matpur.2020.02.008">10.1016/j.matpur.2020.02.008</a>. P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234. 75732020-03-08T23:00:47Z2026-04-08T07:00:03Z