3 papers
math.NA2026
Approximation properties of double complexes
Daniel Førland Holmen, Jan Martin Nordbotten, Jon Eivind Vatne
We consider the simplicial de Rham complex and the Čech-de Rham complex, two bigraded Hilbert complexes whose Hodge-Laplace problems govern spatially coupled problems in mixed dime…
math.AT2024
An abstract approximation tool for mixed-dimensional and equidimensional modeling
Daniel Førland Holmen, Jan Martin Nordbotten, Jon Eivind Vatne
Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a t…
math.AP2022
The Hodge-Laplacian on the Čech-de Rham complex governs coupled problems
Wietse Marijn Boon, Daniel Førland Holmen, Jan Martin Nordbotten +1
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 obser…