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Softw."],"published-print":{"date-parts":[[2022,6,30]]},"abstract":"<jats:p>We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and, in the case of hexahedral cells, not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including arbitrary degree Lagrange, serendipity, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in open-source libraries.<\/jats:p>","DOI":"10.1145\/3524456","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T13:08:43Z","timestamp":1648213723000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":186,"title":["Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes"],"prefix":"10.1145","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4658-2443","authenticated-orcid":false,"given":"Matthew W.","family":"Scroggs","sequence":"first","affiliation":[{"name":"Department of Engineering, Universityof Cambridge, Cambridge, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6489-8858","authenticated-orcid":false,"given":"J\u00f8rgen S.","family":"Dokken","sequence":"additional","affiliation":[{"name":"Department of Engineering, Universityof Cambridge, Cambridge, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3137-1392","authenticated-orcid":false,"given":"Chris N.","family":"Richardson","sequence":"additional","affiliation":[{"name":"BP Institute, University of Cambridge, Cambridge, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5291-7951","authenticated-orcid":false,"given":"Garth N.","family":"Wells","sequence":"additional","affiliation":[{"name":"Department of Engineering, Universityof Cambridge, Cambridge, United Kingdom"}]}],"member":"320","published-online":{"date-parts":[[2022,5,26]]},"reference":[{"issue":"1","key":"e_1_3_2_2_2","first-page":"5","article-title":"On orienting edges of unstructured two- and three-dimensional meshes","volume":"44","author":"Agelek Rainer","year":"2017","unstructured":"Rainer Agelek, Michael Anderson, Wolfgang Bangerth, and William L. 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