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

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

Document type :

Pré-publication ou Document de travail

Title :

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

Author(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]

Publication date :

2024-07-26

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

ANR Project :

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

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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