3 papers
math.NA2026
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…
math.NA2026
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…
math.NA2026
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…