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The Serendipity Family of Finite Elements

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Douglas N. Arnold

  2. Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL, 60115, USA

    Gerard Awanou

Authors
  1. Douglas N. Arnold
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  2. Gerard Awanou
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Corresponding author

Correspondence to Douglas N. Arnold.

Additional information

Communicated by Philippe Ciarlet.

The work of D.N. Arnold was supported in part by NSF grant DMS-0713568.

The work of G. Awanou was supported in part by NSF grant DMS-0811052 and the Sloan Foundation.

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Arnold, D.N., Awanou, G. The Serendipity Family of Finite Elements. Found Comput Math 11, 337–344 (2011). https://doi.org/10.1007/s10208-011-9087-3

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  • DOI: https://doi.org/10.1007/s10208-011-9087-3

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