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dc.contributor.authorHaskovec, Jan
dc.contributor.authorKreusser, Lisa Maria
dc.contributor.authorMarkowich, Peter A.
dc.date.accessioned2019-08-18T12:06:17Z
dc.date.available2019-08-18T12:06:17Z
dc.date.issued2019-05-17
dc.identifier.citationHaskovec, J., Kreusser, L. M., & Markowich, P. (2019). Rigorous continuum limit for the discrete network formation problem. Communications in Partial Differential Equations, 1–27. doi:10.1080/03605302.2019.1612909
dc.identifier.doi10.1080/03605302.2019.1612909
dc.identifier.urihttp://hdl.handle.net/10754/656469
dc.description.abstractMotivated by recent papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption function constrained by a linear system on a graph. For the spatially two-dimensional rectangular setting we prove the rigorous continuum limit of the constrained energy functional as the number of nodes of the underlying graph tends to infinity and the edge lengths shrink to zero uniformly. The proof is based on reformulating the discrete energy functional as a sequence of integral functionals and proving their Γ-convergence towards a continuum energy functional.
dc.description.sponsorshipLMK was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 and the German National Academic Foundation (Studienstiftung des Deutschen Volkes).
dc.publisherInforma UK Limited
dc.relation.urlhttps://www.tandfonline.com/doi/full/10.1080/03605302.2019.1612909
dc.rightsArchived with thanks to Communications in Partial Differential Equations
dc.subjectContinuum limit
dc.subjectΓ-convergence
dc.subjectfinite element discretization
dc.subjectnetwork formation
dc.titleRigorous continuum limit for the discrete network formation problem
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalCommunications in Partial Differential Equations
dc.rights.embargodate2020-01-01
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Cambridge, UK
dc.contributor.institutionFaculty of Mathematics, University of Vienna, Vienna, Austria
kaust.personHaskovec, Jan
kaust.personMarkowich, Peter A.
refterms.dateFOA2020-01-01T00:00:00Z


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