Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 11, Issue 3, Pages 337-344Publisher
SPRINGER
DOI: 10.1007/s10208-011-9087-3
Keywords
Serendipity; Finite element; Unisolvence
Funding
- NSF [DMS-0713568, DMS-0811052]
- Sloan Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1115291] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0811052] Funding Source: National Science Foundation
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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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