Paper Info
Title
Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes
Abstract
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.
Year
DOI
Venue
2022
10.1145/3524456
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
Keywords
DocType
Volume
Finite element methods, degrees-of-freedom, polyhedral cells
Journal
48
Issue
ISSN
Citations 
2
0098-3500
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Matthew W. Scroggs100.34
Jørgen S. Dokken200.34
Chris N. Richardson300.34
Garth N. Wells420220.08