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arXiv · 2211.04556

The Hodge-Laplacian on the \v{C}ech-de Rham complex governs coupled problems

Wietse Marijn Boon·Daniel Førland Holmen·Jan Martin Nordbotten·Jon Eivind Vatne
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Abstract

By endowing the \v{C}ech-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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Wietse Marijn Boon, Daniel Førland Holmen, Jan Martin Nordbotten, Jon Eivind Vatne. 2022-11-08. The Hodge-Laplacian on the \v{C}ech-de Rham complex governs coupled problems. https://arxiv.org/abs/2211.04556

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