The Hodge-Laplacian on the Čech-de Rham complex governs coupled problems

2022/11/08 by Wietse M. Boon, Daniel Førland Holmen, Boon, Wietse Marijn +5 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Analysis of PDEs (math.AP) #FOS: Mathematics #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2211.04556

openalex publication_date 2022/11/08 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28

Abstract

By endowing the Čech-de Rham complex with a Hilbert space structure, we obtain a Hilbert complex with sufficient properties to allow for well-posed Hodge-Laplace problems. We observe that these Hodge-Laplace equations govern a class of coupled problems arising from physical systems including elastically attached strings, multiple-porosity flow systems and 3D-1D coupled flow models.

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