期刊
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
卷 16, 期 4, 页码 667-683出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2016-0019
关键词
Generalized Barycentric Coordinates; Polygonal Finite Element Methods; Finite Element Exterior Calculus
资金
- NSF Award [1522289]
- J. Tinsley Oden Fellowship
- NIH [R01-GM117594]
- Sandia National Labs [BD-4485]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1522289] Funding Source: National Science Foundation
We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nedelec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.
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