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Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator

by R. Dabetic and R. Hiptmair

(Report number 2025-23)

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 Guzmán and Pratyush Potu, A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms, arXiv Preprint 2505.08934, 2025].

Keywords: Hodge-Dirac operator, discrete exterior calculus (DEC), cochains, dual meshes,

@Techreport{DH25_1144,
  author = {R. Dabetic and R. Hiptmair},
  title = {Convergence of Discrete Exterior Calculus for the Hodge-Dirac
Operator},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-23},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-23.pdf },
  year = {2025}
}

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