Small Trees for High Order Whitney Elements

Abstract

AbstractIn applied computations the need arises to define, for example, a discrete field with assigned curl or to represent a div-free field in a given discrete space. In the low degree case this need is often fulfilled by employing tree and co-tree techniques. The definition of tree and co-tree is thus revisited here in the frame of high order Whitney element reconstructions. We consider the case of fields that are reconstructed in a contractible polyhedral domain $$\varOmega \in \mathbb R^3$$ Ω ∈ ℝ 3 , with connected boundary ∂Ω, starting from their weights over suitable “small simplices” in a simplicial mesh $${\mathcal M}$$ ℳ of the domain $$\bar \varOmega $$ Ω ̄ .