Mathematics – Numerical Analysis
Scientific paper
2011-01-04
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.
Arnold Douglas N.
Awanou Gerard
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