Finite element differential forms on cubical meshes

Douglas N. Arnold, Gerard Awanou

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.

Original languageEnglish (US)
Pages (from-to)1551-1570
Number of pages20
JournalMathematics of Computation
Issue number288
StatePublished - 2014


  • Cubes
  • Cubical meshes
  • Finite element differential forms
  • Finite element exterior calculus
  • Mixed finite elements

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