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.
DOI: 10.1051/m2an/2015089
Keywords: finite element systems, differential forms, virtual element methods, Serendipity elements, TNT elements
@article{M2AN_2016__50_3_833_0, author = {Christiansen, Snorre H. and Gillette, Andrew}, title = {Constructions of some minimal finite element systems}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {833--850}, publisher = {EDP-Sciences}, volume = {50}, number = {3}, year = {2016}, doi = {10.1051/m2an/2015089}, mrnumber = {3507275}, zbl = {1343.65135}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015089/} }
TY - JOUR AU - Christiansen, Snorre H. AU - Gillette, Andrew TI - Constructions of some minimal finite element systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 833 EP - 850 VL - 50 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015089/ DO - 10.1051/m2an/2015089 LA - en ID - M2AN_2016__50_3_833_0 ER -
%0 Journal Article %A Christiansen, Snorre H. %A Gillette, Andrew %T Constructions of some minimal finite element systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 833-850 %V 50 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015089/ %R 10.1051/m2an/2015089 %G en %F M2AN_2016__50_3_833_0
Christiansen, Snorre H.; Gillette, Andrew. Constructions of some minimal finite element systems. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 3, pp. 833-850. doi : 10.1051/m2an/2015089. http://www.numdam.org/articles/10.1051/m2an/2015089/
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