Homogenisation of one-dimensional discrete optimal transport Gladbach, Peter Kopfer, Eva Maas, Jan ; https://orcid.org/0000-0002-0845-1338 Portinale, Lorenzo 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. Elsevier 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/7573 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.matpur.2020.02.008 info:eu-repo/semantics/altIdentifier/issn/0021-7824 info:eu-repo/semantics/altIdentifier/wos/000539439400008 info:eu-repo/semantics/altIdentifier/arxiv/1905.05757 info:eu-repo/semantics/openAccess