Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms

Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms

We derive bounds for the constants in Poincaré–Friedrichs inequalities with respect to mesh-dependent norms for complexes of discrete distributional differential forms. A key tool is a generalized flux reconstruction which is of independent interest. The results apply to piecewise polynomial de Rham...

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Veröffentlicht in:BIT 2020-06, Vol.60 (2), p.345-371
Hauptverfasser: Christiansen, Snorre H., Licht, Martin W.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Computational Mathematics and Numerical Analysis
Inequalities
Mathematics
Mathematics and Statistics
Norms
Numeric Computing
Polynomials
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Zusammenfassung:We derive bounds for the constants in Poincaré–Friedrichs inequalities with respect to mesh-dependent norms for complexes of discrete distributional differential forms. A key tool is a generalized flux reconstruction which is of independent interest. The results apply to piecewise polynomial de Rham sequences on bounded domains with mixed boundary conditions.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-019-00784-1