The abstract Hodge-Dirac operator and its stable discretization
| dc.contributor.author | Leopardi, Paul | en |
| dc.contributor.author | Stern, Ari | en |
| dc.date.accessioned | 2025-06-03T08:30:28Z | |
| dc.date.available | 2025-06-03T08:30:28Z | |
| dc.date.issued | 2016 | en |
| dc.description.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), pp. 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. | en |
| dc.description.sponsorship | The work of the first author was supported by the Australian Research Council, the Australian Mathematical Sciences Institute, and the Australian National University. The work of the second author was supported by the Simons Foundation through an AMS-Simons Travel grant and a Collaboration Grant in Mathematics (award 279968). | en |
| dc.description.status | Peer-reviewed | en |
| dc.format.extent | 22 | en |
| dc.identifier.issn | 0036-1429 | en |
| dc.identifier.scopus | 85007107118 | en |
| dc.identifier.uri | http://www.scopus.com/inward/record.url?scp=85007107118&partnerID=8YFLogxK | en |
| dc.identifier.uri | https://hdl.handle.net/1885/733756527 | |
| dc.language.iso | en | en |
| dc.rights | Publisher Copyright: © 2016 Society for Industrial and Applied Mathematics. | en |
| dc.source | SIAM Journal on Numerical Analysis | en |
| dc.subject | Clifford analysis | en |
| dc.subject | Finite element exterior calculus | en |
| dc.subject | Geometric calculus | en |
| dc.subject | Hodge theory | en |
| dc.subject | Hodge-Dirac operator | en |
| dc.title | The abstract Hodge-Dirac operator and its stable discretization | en |
| dc.type | Journal article | en |
| dspace.entity.type | Publication | en |
| local.bibliographicCitation.lastpage | 3279 | en |
| local.bibliographicCitation.startpage | 3258 | en |
| local.contributor.affiliation | Leopardi, Paul; Mathematics Programs, Mathematical Sciences Institute, ANU College of Systems and Society, The Australian National University | en |
| local.contributor.affiliation | Stern, Ari; Washington University St. Louis | en |
| local.identifier.citationvolume | 54 | en |
| local.identifier.doi | 10.1137/15M1047684 | en |
| local.identifier.pure | 08702988-4071-4f8e-82e2-2fa4b5edfc87 | en |
| local.identifier.url | https://www.scopus.com/pages/publications/85007107118 | en |
| local.type.status | Published | en |