Partial differential equations on hypergraphs and networks of surfaces

• Verfasst von: Rupp, Andreas [VerfasserIn]
• Verfasst von: Gahn, Markus [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Titel: Partial differential equations on hypergraphs and networks of surfaces
• Titelzusatz: derivation and hybrid discretizations
• Verf.angabe: Andreas Rupp, Markus Gahn and Guido Kanschat
• E-Jahr: 2022
• Jahr: 24 February 2022
• Umfang: 24 S.
• Fussnoten: Gesehen am 13.04.2022
• Titel Quelle: Enthalten in: Mathematical modelling and numerical analysis
• Ort Quelle: Les Ulis : EDP Sciences, 1999
• Jahr Quelle: 2022
• Band/Heft Quelle: 56(2022), 2 vom: März/Apr., Seite 505-528
• ISSN Quelle: 2804-7214
• DOI: doi:10.1051/m2an/2022011
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1799499812

Abstract

We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces - generalized by the term hypergraphs. To this end, we consider PDEs on hypergraphs as singular limits of PDEs in networks of thin domains (such as fault planes, pipes, etc.), and we observe that (mixed) hybrid formulations offer useful tools to formulate such PDEs. Thus, our numerical framework is based on hybrid finite element methods (in particular, the class of hybrid discontinuous Galerkin methods).