@article{7573,
  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.},
  author       = {Gladbach, Peter and Kopfer, Eva and Maas, Jan and Portinale, Lorenzo},
  issn         = {0021-7824},
  journal      = {Journal de Mathematiques Pures et Appliquees},
  number       = {7},
  pages        = {204--234},
  publisher    = {Elsevier},
  title        = {{Homogenisation of one-dimensional discrete optimal transport}},
  doi          = {10.1016/j.matpur.2020.02.008},
  volume       = {139},
  year         = {2020},
}