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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Bibliographic Details
Published in:	BIT Vol. 60; no. 2; pp. 345 - 371
Main Authors:	Christiansen, Snorre H., Licht, Martin W.
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01-06-2020 Springer Nature B.V BMJ Publishing Group
Subjects:	Boundary conditions Computational Mathematics and Numerical Analysis Inequalities Mathematics Mathematics and Statistics Norms Numeric Computing Polynomials Finite element method Homology theory Finite element exterior calculus Discrete distributional differential form Poincaré–Friedrichs inequality 65N30
Online Access:	Get full text
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Summary:	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