Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods
Numerical Analysis
2021-12-08 v2 Numerical Analysis
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.
Cite
@article{arxiv.2106.01693,
title = {Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods},
author = {T. Chaumont-Frelet and A. Ern and S. Lemaire and F. Valentin},
journal= {arXiv preprint arXiv:2106.01693},
year = {2021}
}