Foundations of Computational Mathematics

, Volume 11, Issue 3, pp 337–344

The Serendipity Family of Finite Elements


DOI: 10.1007/s10208-011-9087-3

Cite this article as:
Arnold, D.N. & Awanou, G. Found Comput Math (2011) 11: 337. doi:10.1007/s10208-011-9087-3


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 sr 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.


SerendipityFinite elementUnisolvence

Mathematics Subject Classification (2000)


Copyright information

© SFoCM 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Mathematical SciencesNorthern Illinois UniversityDekalbUSA