Higher ORDER Whitney Forms

The calculus of differential forms can be used to devise a unified description of discrete differential forms of any order and polynomial degree on simplicial meshes in any spatial dimension. A general formula for suitable degrees of freedom is also available. Fundamental properties of nodal interpolation can be established easily. It turns out that higher order spaces, including variants with locally varying polynomial order, emerge from the usual Whitney-forms by local augmentation. This paves the way for an adaptive p-version approach to discrete differential forms.