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dc.contributor.authorBoon, Wietse
dc.contributor.authorNordbotten, Jan Martin
dc.contributor.authorVatne, Jon Eivind
dc.identifier.citationBoon, W. M., Nordbotten, J. M., & Vatne, J. E. (2020). Functional analysis and exterior calculus on mixed-dimensional geometries. Annali Di Matematica Pura Ed Applicata, 2020.en_US
dc.description.abstractWe are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of d-dimensional manifolds, structured hierarchically so that each d-dimensional manifold is contained in the boundary of one or more d+1-dimensional manifolds. On any given d-dimensional manifold, we then consider differential operators tangent to the manifold as well as discrete differential operators (jumps) normal to the manifold. The combined action of these operators leads to the notion of a semi-discrete differential operator coupling manifolds of different dimensions. We refer to the resulting systems of equations as mixed-dimensional, which have become a popular modeling technique for physical applications including fractured and composite materials. We establish analytical tools in the mixed-dimensional setting, including suitable inner products, differential and codifferential operators, Poincaré lemma, and Poincaré–Friedrichs inequality. The manuscript is concluded by defining the mixed-dimensional minimization problem corresponding to the Hodge Laplacian, and we show that this minimization problem is well-posed.en_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.subjectmixed-dimensional diferential operatorsen_US
dc.subjectmixed-dimensional geometryen_US
dc.subjectexterior calculusen_US
dc.titleFunctional analysis and exterior calculus on mixed-dimensional geometriesen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.rights.holder© The Author(s) 2020en_US
dc.subject.nsiVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410en_US
dc.source.journalAnnali di Matematica Pura ed Applicataen_US
dc.relation.projectNorges forskningsråd: 250223en_US
dc.relation.projectNorges forskningsråd: 233736en_US

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