Douglas N. Arnold, Gerard Awanou
Published 2012-04-12, updated 2013-07-30Version 3
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.
Comments: v2: as accepted by Mathematics of Computation after minor revisions; v3: this version corresponds to the final version for Math. Comp., after copyediting and galley proofs
Spaces of finite element differential forms
On Basis Constructions in Finite Element Exterior Calculus
Finite element exterior calculus for parabolic problems
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