Affiliation:
1. Department of Engineering, Universityof Cambridge, Cambridge, United Kingdom
2. BP Institute, University of Cambridge, Cambridge, United Kingdom
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference34 articles.
1. On orienting edges of unstructured two- and three-dimensional meshes;Agelek Rainer;ACM Transactions on Mathematical Software,2017
2. Hierarchic finite element bases on unstructured tetrahedral meshes
3. The FEniCS project version 1.5;Alnæs Martin S.;Archive of Numerical Software,2015
4. Lecture Notes in Computational Science and Engineering;Alnæs Martin S.,2012
5. Unified form language
Cited by
78 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献