Geodesic
Constructions of some minimal finite element systems
Christiansen, Snorre H.1  ; Gillette, Andrew2
1 Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway
2 Department of Mathematics, University of Arizona, PO Box 210089, Tucson, Arizona, USA
ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 833-850

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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.

Reçu le :
DOI : 10.1051/m2an/2015089
Classification : 65N30
Keywords: finite element systems, differential forms, virtual element methods, Serendipity elements, TNT elements

Christiansen, Snorre H. 1 ; Gillette, Andrew 2

1 Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway
2 Department of Mathematics, University of Arizona, PO Box 210089, Tucson, Arizona, USA 
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Christiansen, Snorre H.; Gillette, Andrew. Constructions of some minimal finite element systems. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 833-850. doi: 10.1051/m2an/2015089

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