Hybrid high-order approximations of div-curl systems on domains with general topology

Dalphin, Jérémy; Ducreux, Jean-Pierre; Lemaire, Simon; Pitassi, Silvano

Type de document :

Pré-publication ou Document de travail

Titre :

Hybrid high-order approximations of div-curl systems on domains with general topology

Auteur(s) :

Dalphin, Jérémy [Auteur]
ElectRotechnique et MEcanique des Structures [EDF R&D ERMES]
Ducreux, Jean-Pierre [Auteur]

ElectRotechnique et MEcanique des Structures [EDF R&D ERMES]
Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Pitassi, Silvano [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
ElectRotechnique et MEcanique des Structures [EDF R&D ERMES]

Date de publication :

2024-07-26

Mot(s)-clé(s) en anglais :

Div-curl systems
Polyhedral meshes
Hybrid methods
de Rham cohomology
Computational topology

Discipline(s) HAL :

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

Résumé en anglais : [en]

We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The systems we focus on stem from magnetostatics ...
Lire la suite >We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The systems we focus on stem from magnetostatics models, and can either be first-order (field formulation) or second-order (vector potential formulation). The well-posedness of our methods essentially relies on topologically general discrete (hybrid) versions of the first and second Weber inequalities. In turn, our error analysis is performed under low regularity assumptions on the solutions. Finally, we provide a comprehensive numerical validation of our methodology.Lire moins >

Langue :

Anglais

Projet ANR :

Méthodes polyédriques d'ordre élevé pour la simulation du contrôle non-destructif par courants de Foucault
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

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