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.
Original language | English (US) |
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Pages (from-to) | 337-344 |
Number of pages | 8 |
Journal | Foundations of Computational Mathematics |
Volume | 11 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2011 |
Bibliographical note
Funding Information:The work of G. Awanou was supported in part by NSF grant DMS-0811052 and the Sloan Foundation.
Funding Information:
The work of D.N. Arnold was supported in part by NSF grant DMS-0713568.
Keywords
- Finite element
- Serendipity
- Unisolvence