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The Abstract Hodge--Dirac Operator and Its Stable Discretization
2016
SIAM Journal on Numerical Analysis
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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
doi:10.1137/15m1047684
fatcat:bwm7twylwjg6xm4wfojjbbj4sa