The abstract Hodge-Dirac operator and its stable discretization

Presenter: Paul Leopardi, The Australian National University, Australia

Joint work with Ari Stern, WUSTL

We adapt 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 (2010). We give 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. See the preprint arXiv:1401.1576 [math.NA] for details.

Software presentation – FEniCS and GluCat/PyClical

Paul Leopardi, The Australian National University, Australia