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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2022

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

Abstract

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 term. 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. We also leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.
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Dates and versions

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

Identifiers

Cite

Théophile Chaumont-Frelet, Alexandre Ern, Simon Lemaire, Frédéric Valentin. Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (1), pp.261-285. ⟨10.1051/m2an/2021082⟩. ⟨hal-03235525v3⟩
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