TY - JOUR
T1 - Constructions of some minimal finite element systems
AU - Christiansen, Snorre H.
AU - Gillette, Andrew
N1 - Funding Information:
SHC was supported by the European Research Council through the FP7-IDEAS-ERC Starting Grant scheme, Project 278011 STUCCOFIELDS. AG was supported in part by NSF Award 1522289.
Publisher Copyright:
© 2016 EDP Sciences, SMAI.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these constraints. We show how various known mixed finite element spaces fulfill such a design principle, including trimmed polynomial differential forms, serendipity elements and TNT elements. We also comment on virtual element methods and provide a dimension formula for minimal compatible finite element systems containing polynomials of a given degree on hypercubes.
AB - Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these constraints. We show how various known mixed finite element spaces fulfill such a design principle, including trimmed polynomial differential forms, serendipity elements and TNT elements. We also comment on virtual element methods and provide a dimension formula for minimal compatible finite element systems containing polynomials of a given degree on hypercubes.
KW - Differential forms
KW - Finite element systems
KW - Serendipity elements
KW - TNT elements
KW - Virtual element methods
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U2 - 10.1051/m2an/2015089
DO - 10.1051/m2an/2015089
M3 - Article
AN - SCOPUS:84971458090
SN - 2822-7840
VL - 50
SP - 833
EP - 850
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 3
ER -