The Multiscale Hybrid Mixed Method in General Polygonal Meshes - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2019

The Multiscale Hybrid Mixed Method in General Polygonal Meshes

Résumé

This work extends the general form of the Multiscale Hybrid-Mixed (MHM) method for the second-order Laplace (Darcy) equation to general non-conforming polygonal meshes. The main properties of the MHM method, i.e., stability, optimal convergence, and local conservation, are proven independently of the geometry of the elements used for the first level mesh. More precisely, it is proven that piecewise polynomials of degree k and k + 1, k ≥ 0, for the Lagrange multipliers (flux), along with continuous piecewise polynomial interpolations of degree k + 1 posed on second-level sub-meshes are stable if the latter is fine enough with respect to the mesh for the Lagrange multiplier. We provide an explicit sufficient condition for this restriction. Also, we prove that the error converges with order k + 1 and k + 2 in the broken H 1 and L 2 norms, respectively, under usual regularity assumptions, and that such estimates also hold for non-convex; or even non-simply connected elements. Numerical results confirm the theoretical findings and illustrate the gain that the use of multiscale functions provides.
Fichier principal
Vignette du fichier
BJPV18.pdf (3.96 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02054681 , version 1 (02-03-2019)

Identifiants

  • HAL Id : hal-02054681 , version 1

Citer

Gabriel R Barrenechea, Fabrice Jaillet, Diego Paredes, Frédéric Valentin. The Multiscale Hybrid Mixed Method in General Polygonal Meshes. [Research Report] LNCC - Laboratorio Nacional de Computacao Cientifica. 2019. ⟨hal-02054681⟩
132 Consultations
177 Téléchargements

Partager

Gmail Facebook X LinkedIn More