Discrete Weber inequalities and related ...
Document type :
Pré-publication ou Document de travail
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]
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
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 >
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 >
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Anglais
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