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The Hodge-Laplacian on the \v{C}ech-de Rham complex governs coupled problems
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math.AP
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complexcoupledproblemsech-deflowhilberthodge-laplacerham
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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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