5 papers
Discrete Poincaré and Bogovskii operators for higher order finite element de Rham complexes
Johnny Guzmán, Pratyush Potu, K. Olav Tyssvang
We present discrete Poincaré and Bogovskii operators for the common finite element discretizations of the de Rham complex of arbitrary polynomial order. We first discuss how such o…
Bounded, Commuting, Discrete-trace Preserving Projections
Alexandre Ern, Johnny Guzmán, Pratyush Potu
We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if th…
Discrete Poincare and Bogovskii operators on cochains and Whitney forms
Johnny Guzmán, Anil N. Hirani, Bingyan Liu +1
Smooth Poincare operators are a tool used to show the vanishing of smooth de Rham cohomology on contractible manifolds and have found use in the analysis of finite element methods…
A local Fortin projection for the Scott-Vogelius elements on general meshes
Franziska Eickmann, Johnny Guzmán, Michael Neilan +2
We construct a local Fortin projection for the Scott-Vogelius finite element pair for polynomial degree on general shape-regular triangulations in two dimensions. In part…
Local -bounded commuting projections in FEEC
Douglas N. Arnold, Johnny Gúzman
We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in and commute with the…