Constructions of some minimal finite element systems

Snorre H. Christiansen, Andrew Gillette

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)833-850
Number of pages18
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number3
StatePublished - May 1 2016


  • Differential forms
  • Finite element systems
  • Serendipity elements
  • TNT elements
  • Virtual element methods

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics


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