The serendipity family of finite elements

Details The serendipity family of finite elements The serendipity family of finite elements

2011-01-04

arxiv.org/abs/1101.0645v1

Mathematics

Numerical Analysis

7 pages, 1 figure, 1 table. To appear in Foundations in Computational Mathematics, 2011

Scientific paper

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.

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