Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator
arXiv:2507.1940542.9h-index: 1
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This is an incremental theoretical contribution for researchers in numerical analysis and computational geometry, extending existing convergence proofs to a related operator.
The paper provides a short proof of convergence for the discretization of the Hodge-Dirac operator using discrete exterior calculus (DEC), building on prior work for Hodge-Laplacian problems.
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:2505.08934, 2025]