A category theoretical interpretation of discretization in Galerkin finite element method

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorLahtinen, Valtteri
dc.contributor.authorStenvall, Antti
dc.contributor.departmentDepartment of Applied Physics
dc.contributor.departmentTampere University
dc.date.accessioned2021-03-10T07:25:55Z
dc.date.available2021-03-10T07:25:55Z
dc.date.issued2020-12-01
dc.description.abstractThe Galerkin finite element method (FEM) is used widely in finding approximative solutions to field problems in engineering and natural sciences. When utilizing FEM, the field problem is said to be discretized. In this paper, we interpret discretization in FEM through category theory, unifying the concept of discreteness in FEM with that of discreteness in other fields of mathematics, such as topology. This reveals structural properties encoded in this concept: we propose that discretization is a dagger mono with a discrete domain in the category of Hilbert spaces made concrete over the category of vector spaces. Moreover, we discuss parallel decomposability of discretization, and through examples, connect it to different FEM formulations and choices of basis functions.en
dc.description.versionPeer revieweden
dc.format.extent15
dc.format.extent1271-1285
dc.format.mimetypeapplication/pdf
dc.identifier.citationLahtinen , V & Stenvall , A 2020 , ' A category theoretical interpretation of discretization in Galerkin finite element method ' , MATHEMATISCHE ZEITSCHRIFT , vol. 296 , no. 3-4 , pp. 1271-1285 . https://doi.org/10.1007/s00209-020-02456-1en
dc.identifier.doi10.1007/s00209-020-02456-1
dc.identifier.issn0025-5874
dc.identifier.issn1432-1823
dc.identifier.otherPURE UUID: 16fa2be0-30f9-473c-ab4d-fcf66e5e4a4d
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/16fa2be0-30f9-473c-ab4d-fcf66e5e4a4d
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85078401561&partnerID=8YFLogxK
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/56811698/Lahtinen_Stenvall2020_Article_ACategoryTheoreticalInterpreta.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/102939
dc.identifier.urnURN:NBN:fi:aalto-202103102225
dc.language.isoenen
dc.publisherSPRINGER HEIDELBERG
dc.relation.ispartofseriesMATHEMATISCHE ZEITSCHRIFTen
dc.relation.ispartofseriesVolume 296, issue 3-4en
dc.rightsopenAccessen
dc.subject.keywordCategory theory
dc.subject.keywordDiscretization
dc.subject.keywordEngineering
dc.subject.keywordFinite element method
dc.subject.keywordMathematical modeling
dc.titleA category theoretical interpretation of discretization in Galerkin finite element methoden
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
Files