Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator

TL;DR

This paper provides a concise proof demonstrating the convergence of the discretized Hodge-Dirac operator within discrete exterior calculus, building on established analytical techniques.

Contribution

It offers a new, simplified convergence proof for the discretization of the Hodge-Dirac operator in DEC, enhancing theoretical understanding.

Findings

Proof of convergence for the discretized Hodge-Dirac operator

Utilizes techniques from Guzmán and Potu's framework

Strengthens theoretical foundation of DEC methods

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]