Geometrical localisation of the degrees of freedom for whitney elements of higher order

Low-order Whitney forms are widely used for electromagnetic field problems. Higher-order ones are increasingly applied, but their development is hampered by the complexity of the generation of element basis functions and of the localisation of the corresponding degrees of freedom on the mesh volumes. The paper aims to give a geometrical localisation of the degrees of freedom associated with Whitney forms of a polynomial degree higher than one. A conveniently implementable basis is provided for these elements on simplicial meshes. As for Whitney forms of degree one, the basis is expressed only in terms of the barycentric co-ordinates of the simplex