Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator
Numerical Analysis
2026-05-01 v2 Numerical Analysis
Abstract
A short proof of convergence for the discretization of the Hodge-Dirac operator in the framework of discrete exterior calculus (DEC) is provided using the techniques established in [Johnny Guzm\'an and Pratyush Potu, A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms, arXiv:2505.08934, 2025]
Cite
@article{arxiv.2507.19405,
title = {Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator},
author = {Radovan Dabetić and Ralf Hiptmair},
journal= {arXiv preprint arXiv:2507.19405},
year = {2026}
}
Comments
Changes: Minor stylistic revisions, updated figures (fixed minor bugs in the code), and added some additional comments and references