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

Chaumont-Frelet, Théophile; Ern, Alexandre; Lemaire, Simon; Valentin, Frédéric

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1051/m2an/2021082

Title :

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

Author(s) :

Chaumont-Frelet, Théophile [Auteur]
Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée [ATLANTIS]
Ern, Alexandre [Auteur]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Valentin, Frédéric [Auteur]
Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée [ATLANTIS]
Laboratorio Nacional de Computação Cientifica [Rio de Janeiro] [LNCC / MCT]

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

261-285

Publisher :

Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP

Publication date :

2022

ISSN :

2822-7840

English keyword(s) :

Highly heterogeneous diffusion
Multiscale methods
General polytopal meshes
High-order methods

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :