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math.NA2025
Finite Element Spaces of Double Two-Forms With Polynomial Coefficients
Yakov Berchenko-Kogan, Lily DiPaulo
We develop finite element spaces of symmetric tensor products of two-forms with polynomial coefficients. In three dimensions, these give higher order finite element spaces of matri…
math.NA2025
Finite element spaces of double forms
Yakov Berchenko-Kogan, Evan S. Gawlik
The tensor product of two differential forms of degree and is a multilinear form that is alternating in its first arguments and alternating in its last arguments. T…
math.NA2025
Extension operators and geometric decompositions
Yakov Berchenko-Kogan
Geometric decomposition is a widely used tool for constructing local bases for finite element spaces. For finite element spaces of differential forms on simplicial meshes, Arnold,…