  This paper adapts the techniques of finite element exterior calculus to study
and discretize the abstract Hodge-Dirac operator, which is a square root of the
abstract Hodge-Laplace operator considered by Arnold, Falk, and Winther [Bull.
Amer. Math. Soc. 47 (2010), 281-354]. Dirac-type operators are central to the
field of Clifford analysis, where recently there has been considerable interest
in their discretization. We prove a priori stability and convergence estimates,
and show that several of the results in finite element exterior calculus can be
recovered as corollaries of these new estimates.
