A systematic construction of finite element commuting exact sequences

Bernardo Cockburn, Guosheng Fu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We present a systematic construction of finite element exact sequences with a commuting diagram property for the de Rham complex in one-, two-, and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in three-space dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms, and to uncover four new families of exact sequences for pyramids, three for prisms, and one for cubes.

Original languageEnglish (US)
Pages (from-to)1650-1688
Number of pages39
JournalSIAM Journal on Numerical Analysis
Volume55
Issue number4
DOIs
StatePublished - Jan 1 2017

Keywords

  • Commuting diagrams
  • Exact sequences
  • Finite elements
  • Polyhedral elements

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