High order edge elements for Maxwell’s equations: construction and properties

Marcella Bonazzoli, Elena Gaburro

University of Verona


Low order edge finite elements are widely used for electromagnetic problems and high order edge approximations are receiving increasing interest. Most of the existing extensions of Whitney first order edge elements rely on higher and higher moments to define the needed degrees of freedom (dofs). As a result, such high order extensions include non-physical dofs (like face or volume moments) that are not easy to interpret as field circulations along edges which are the dofs in the first order case. I present here a definition which removes this inconvenience: the basis functions are products of first order edge element basis functions by suitable monomials in the barycentric coordinate functions of the triangle. This construction is based on “small edges” associated with the principal lattice of the triangle and defined by means of a particular homothety. These elements can be used in practice: even with a coarse mesh a small error is obtained and a good order of convergence is achieved.