Whitney Forms of Higher Degree

Low order Whitney elements are widely used for electromagnetic field problems. Higher order approximations are receiving increasing interest but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to p-chains. We provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom. Properties of the higher-order Whitney complex are deeply investigated.