The Hodge-Laplacian on the Čech-de Rham complex governs coupled problems
Wietse M. Boon, Daniel Førland Holmen, Jan Martin Nordbotten, Jon Eivind Vatne · Journal of Mathematical Analysis and Applications · 2025
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 rods, multiple-porosity flow systems and 3D-1D coupled flow models.