A $C^1$ Tetrahedral Finite Element without Edge Degrees of Freedom

A composite $C^1$ tetrahedral finite element is developed which does not have any edge degrees of freedom. This eliminates the need to associate a basis for the planes perpendicular to each edge; such a basis cannot depend continuously upon the edge orientation. The finite element space is piecewise...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2014-01, Vol.52 (1), p.330-342
Main Author: Walkington, Noel J.
Format: Article
Language:English
Subjects:
Polynomials
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Summary:A composite $C^1$ tetrahedral finite element is developed which does not have any edge degrees of freedom. This eliminates the need to associate a basis for the planes perpendicular to each edge; such a basis cannot depend continuously upon the edge orientation. The finite element space is piecewise polynomial over the four tetrahedra formed by adding the circumcenter, and their traces on each face belong to the (two-dimensional) Bell subspace. [PUBLICATION ABSTRACT]
ISSN:0036-1429
1095-7170
DOI:10.1137/130912013