The Abstract Hodge--Dirac Operator and Its Stable Discretization

Paul Leopardi, Ari Stern
2016 SIAM Journal on Numerical Analysis  
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
more » ... the results in finite element exterior calculus can be recovered as corollaries of these new estimates.
doi:10.1137/15m1047684 fatcat:bwm7twylwjg6xm4wfojjbbj4sa