High order edge elements on simplicial meshes

Rapetti, Francesca

ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 1001-1020.

Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex. In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one. We give a geometrical localization of all degrees of freedom over particular edges and provide a basis for these elements on simplicial meshes. As for Whitney edge elements of degree one, the basis is expressed only in terms of the barycentric coordinates of the simplex.

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