LAUSR

We consider a family of geometrical objects first evocated around 1952 by André Weil with reference to the work of de Rham, but deeply analyzed in 1957 by Whitney (Hassler Whitney, 1907–1989, one of the masters of differential geometry), thus known in the literature as “Whitney (differential) forms,” and we comment on its high-order extension. They constitute the right framework in which to develop a finite element discretization of electromagnetic theory. The high-order generalization we consider has been realized by refining the chains that describe the manifolds and using the duality of Whitney forms. When rising up the polynomial degree of the forms, from 1 to $k+1$ with $k>0$, this construction satisfies the same combinatorial and topological properties of the Whitney complex of polynomial degree 1.