Serendipity and Tensor Product Affine Pyramid Finite Elements
The SMAI journal of computational mathematics, Volume 2 (2016) , pp. 215-228.

Using the language of finite element exterior calculus, we define two families of ${H}^{1}$-conforming finite element spaces over pyramids with a parallelogram base. The first family has matching polynomial traces with tensor product elements on the base while the second has matching polynomial traces with serendipity elements on the base. The second family is new to the literature and provides a robust approach for linking between Lagrange elements on tetrahedra and serendipity elements on affinely-mapped cubes while preserving continuity and approximation properties. We define shape functions and degrees of freedom for each family and prove unisolvence and polynomial reproduction results.

Published online:
DOI: https://doi.org/10.5802/smai-jcm.14
Classification: 65N30,  41A20,  41A10
Keywords: Finite element methods; pyramid elements; rational functions
@article{SMAI-JCM_2016__2__215_0,
author = {Andrew Gillette},
title = {Serendipity and {Tensor} {Product} {Affine} {Pyramid} {Finite} {Elements}},
journal = {The SMAI journal of computational mathematics},
pages = {215--228},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {2},
year = {2016},
doi = {10.5802/smai-jcm.14},
mrnumber = {3633550},
zbl = {1416.65445},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.14/}
}
Andrew Gillette. Serendipity and Tensor Product Affine Pyramid Finite Elements. The SMAI journal of computational mathematics, Volume 2 (2016) , pp. 215-228. doi : 10.5802/smai-jcm.14. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.14/

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