4 papers
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…
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…
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,…
Blow-up Whitney forms, shadow forms, and Poisson processes
Yakov Berchenko-Kogan, Evan S. Gawlik
The Whitney forms on a simplex admit high-order generalizations that have received a great deal of attention in numerical analysis. Less well-known are the shadow forms of Bras…