Commuting diagrams for the tnt elements on cubes

Bernardo Cockburn, Weifeng Qiu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We present commuting diagrams for the de Rham complex for new elements defined on cubes which use tensor product spaces. The distinctive feature of these elements is that, in sharp contrast with previously known results, they have the TiNiest spaces containing Tensor product spaces of polynomials of degree k, hence their acronym TNT. In fact, the local spaces of the TNT elements differ from the standard tensor product spaces by spaces whose dimension is a small number independent of the degree k. Such a number is 7 (the number of vertices of the cube minus one) for the space associated with the divergence operator, 18 (the number of faces of the cube times the number of vertices of a face minus one) for the space associated with the curl operator, and 12 (the number of edges of the cube times the number of vertices of an edge minus one) for the space associated with the gradient operator.

Original languageEnglish (US)
Pages (from-to)603-633
Number of pages31
JournalMathematics of Computation
Volume83
Issue number286
DOIs
StatePublished - Jan 13 2014

Keywords

  • Commuting diagrams
  • Cubic element
  • Tensor product spaces

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