Volume 56, Number 1, January-February 2022
|Page(s)||261 - 285|
|Published online||10 February 2022|
Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods
Université Côte d’Azur, Inria, CNRS, LJAD, 06902 Sophia, Antipolis Cedex, France
2 CERMICS, École des Ponts, 77455 Marne-la-Vallée Cedex 2, France
3 Inria, 2 rue Simone Iff, 75589 Paris, France
4 Inria, Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, 59000 Lille, France
5 LNCC – National Laboratory for Scientific Computing, Av. Getúlio Vargas, 333, 25651-070 Petrópolis – RJ, Brazil
* Corresponding author: email@example.com
Accepted: 9 December 2021
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.
Mathematics Subject Classification: 65N30 / 65N08 / 65N12 / 76R50
Key words: Highly heterogeneous diffusion / multiscale methods / general polytopal meshes / high-order methods
© The authors. Published by EDP Sciences, SMAI 2022
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