Volume 50, Number 3, May-June 2016
Special Issue – Polyhedral discretization for PDE
|Page(s)||833 - 850|
|Published online||23 May 2016|
Constructions of some minimal finite element systems
Department of Mathematics, University of Oslo,
PO Box 1053 Blindern,
2 Department of Mathematics, University of Arizona, PO Box 210089, Tucson, Arizona, USA
Received: 17 April 2015
Revised: 20 October 2015
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.
Mathematics Subject Classification: 65N30
Key words: finite element systems / differential forms / virtual element methods / Serendipity elements / TNT elements
© EDP Sciences, SMAI 2016
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