Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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), pp. 281--354]. Dirac-type operators are central to the field of Clifford analysis, where recently there has been considerable interest in their discretization.  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. (A corrected version is attached.)
['Paul C. Leopardi', 'Ari Stern']
I am writing a research paper on a idea The abstract Hodge-Dirac operator and its stable discretization
[{"from": "human", "value": "I am writing a research paper on a idea The abstract Hodge-Dirac operator and its stable discretization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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), pp. 281--354]. Dirac-type operators are central to the field of Clifford analysis, where recently there has been considerable interest in their discretization.  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. (A corrected version is attached.)"}]