Foundations of Computational Mathematics

, Volume 11, Issue 3, pp 337-344

First online:

The Serendipity Family of Finite Elements

  • Douglas N. ArnoldAffiliated withDepartment of Mathematics, University of Minnesota Email author 
  • , Gerard AwanouAffiliated withDepartment of Mathematical Sciences, Northern Illinois University

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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 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.


Serendipity Finite element Unisolvence

Mathematics Subject Classification (2000)