5 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,…
Numerically computing the index of mean curvature flow self-shrinkers
Yakov Berchenko-Kogan
Surfaces that evolve by mean curvature flow develop singularities. These singularities can be modeled by self-shrinkers, surfaces that shrink by dilations under the flow. Singulari…
The entropy of the Angenent torus is approximately 1.85122
Yakov Berchenko-Kogan
To study the singularities that appear in mean curvature flow, one must understand self-shrinkers, surfaces that shrink by dilations under mean curvature flow. The simplest example…