The serendipity family of finite elements
Numerical Analysis
2014-01-29 v1
Abstract
We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s-r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r-2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Keywords
Cite
@article{arxiv.1101.0645,
title = {The serendipity family of finite elements},
author = {Douglas N. Arnold and Gerard Awanou},
journal= {arXiv preprint arXiv:1101.0645},
year = {2014}
}
Comments
7 pages, 1 figure, 1 table. To appear in Foundations in Computational Mathematics, 2011