{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1905.05757"}],"abstract":[{"lang":"eng","text":"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."}],"department":[{"_id":"JaMa"}],"issue":"7","date_published":"2020-07-01T00:00:00Z","publication_status":"published","date_updated":"2023-09-07T13:31:05Z","article_processing_charge":"No","month":"07","day":"01","type":"journal_article","status":"public","related_material":{"record":[{"id":"10030","relation":"dissertation_contains","status":"public"}]},"quality_controlled":"1","title":"Homogenisation of one-dimensional discrete optimal transport","scopus_import":"1","publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2020-03-08T23:00:47Z","oa_version":"Preprint","oa":1,"_id":"7573","language":[{"iso":"eng"}],"citation":{"short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234.","ista":"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.","chicago":"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>.","apa":"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>","ama":"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>","ieee":"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.","mla":"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>."},"article_type":"original","ec_funded":1,"publication_identifier":{"issn":["00217824"]},"external_id":{"arxiv":["1905.05757"],"isi":["000539439400008"]},"author":[{"full_name":"Gladbach, Peter","last_name":"Gladbach","first_name":"Peter"},{"full_name":"Kopfer, Eva","first_name":"Eva","last_name":"Kopfer"},{"orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale"}],"publication":"Journal de Mathematiques Pures et Appliquees","doi":"10.1016/j.matpur.2020.02.008","page":"204-234","project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"call_identifier":"FWF","grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"isi":1,"acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","year":"2020","volume":139,"intvolume":"       139"}