Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques

In this paper some structures which underlie the numerical treatment of sec ond-order boundary value problems are studied using magnetostatics as an ex ample. We show that the construction of a discrete Hedge is a central probl em. In this light we interpret finite element techniques as a realization o f the discrete Hedge operator in the Whitney complex. This enables us to vi ew the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances.