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.
Keywords: Highly heterogeneous diffusion, multiscale methods, general polytopal meshes, high-order methods
@article{M2AN_2022__56_1_261_0,
author = {Chaumont-Frelet, Th\'eophile and Ern, Alexandre and Lemaire, Simon and Valentin, Fr\'ed\'eric},
title = {Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {261--285},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {1},
doi = {10.1051/m2an/2021082},
mrnumber = {4378547},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021082/}
}
TY - JOUR AU - Chaumont-Frelet, Théophile AU - Ern, Alexandre AU - Lemaire, Simon AU - Valentin, Frédéric TI - Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 261 EP - 285 VL - 56 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021082/ DO - 10.1051/m2an/2021082 LA - en ID - M2AN_2022__56_1_261_0 ER -
%0 Journal Article %A Chaumont-Frelet, Théophile %A Ern, Alexandre %A Lemaire, Simon %A Valentin, Frédéric %T Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 261-285 %V 56 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021082/ %R 10.1051/m2an/2021082 %G en %F M2AN_2022__56_1_261_0
Chaumont-Frelet, Théophile; Ern, Alexandre; Lemaire, Simon; Valentin, Frédéric. Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 1, pp. 261-285. doi: 10.1051/m2an/2021082
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