The abstract Hodge-Dirac operator and its stable discretization
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2014
- DOI:
- 10.48550/arXiv.1401.1576
- arXiv:
- arXiv:1401.1576
- Bibcode:
- 2014arXiv1401.1576L
- Keywords:
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- Mathematics - Numerical Analysis;
- 65N30;
- 58A14
- E-Print:
- 21 pages, 1 figure