Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2021

Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods

Résumé

We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source terms. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. Also, we leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.
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Dates et versions

hal-03235525 , version 1 (25-05-2021)
hal-03235525 , version 2 (07-12-2021)
hal-03235525 , version 3 (07-01-2022)

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Théophile Chaumont-Frelet, Alexandre Ern, Simon Lemaire, Frédéric Valentin. Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. 2021. ⟨hal-03235525v1⟩
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