Title :

Discrete Weber inequalities and related Maxwell compactness for hybrid spaces over polyhedral partitions of domains with general topology

Author(s) :

Lemaire, Simon [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Pitassi, Silvano [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Publication date :

2023-04-25

English keyword(s) :

Weber inequalities
Maxwell compactness
Hybrid polynomial spaces
Polyhedral meshes
de Rham cohomology
Topology
Maxwell's equations

HAL domain(s) :

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

English abstract : [en]

We prove discrete versions of the first and second Weber inequalities on $\boldsymbol{H}({\bf curl})\cap\boldsymbol{H}({\rm div}_\eta)$-like hybrid spaces spanned by polynomials attached to the faces and to the cells of a ...
Show more >We prove discrete versions of the first and second Weber inequalities on $\boldsymbol{H}({\bf curl})\cap\boldsymbol{H}({\rm div}_\eta)$-like hybrid spaces spanned by polynomials attached to the faces and to the cells of a polyhedral mesh. The proven hybrid Weber inequalities are optimal in the sense that (i) they are formulated in terms of $\boldsymbol{H}({\bf curl})$- and $\boldsymbol{H}({\rm div}_\eta)$-like hybrid semi-norms designed so as to embed optimally (polynomially) consistent face penalty terms, and (ii) they are valid for face polynomials in the smallest possible stability-compatible spaces. Our results are valid on domains with general, possibly non-trivial topology. In a second part we also prove, within a general topological setting, related discrete Maxwell compactness properties.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL