caa a22 4500 445331550 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10208-011-9087-3 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9087-3 The Serendipity Family of Finite Elements [Elektronische Daten] [Douglas Arnold, Gerard Awanou] 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. SFoCM, 2011 Serendipity nationallicence Finite element nationallicence Unisolvence nationallicence Arnold Douglas Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut Awanou Gerard Department of Mathematical Sciences, Northern Illinois University, 60115, Dekalb, IL, USA aut Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 337-344 1615-3375 11:3<337 2011 11 10208 https://doi.org/10.1007/s10208-011-9087-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9087-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arnold Douglas Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 700 1- Awanou Gerard Department of Mathematical Sciences, Northern Illinois University, 60115, Dekalb, IL, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 337-344 1615-3375 11:3<337 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer