Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Found Comput Math DOI 10.1007/s10208-011-9087-3
 

Summary: Found Comput Math
DOI 10.1007/s10208-011-9087-3
The Serendipity Family of Finite Elements
Douglas N. Arnold Gerard Awanou
Received: 23 February 2010 / Accepted: 19 November 2010
SFoCM 2011
Abstract We give a new, simple, dimension-independent definition of the serendip-
ity 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.
Keywords Serendipity Finite element Unisolvence
Mathematics Subject Classification (2000) Primary 65N30
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.
D.N. Arnold ( )

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics