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Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, PO Box 1053, 0316, Blindern, Norway

    Snorre H. Christiansen

  2. UCSD Department of Mathematics, 9500 Gilman Drive MC0112, La Jolla, CA, 92093-0112, USA

    Martin W. Licht

Authors
  1. Snorre H. Christiansen
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  2. Martin W. Licht
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Correspondence to Martin W. Licht.

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This research was supported by the European Research Council through the FP7-IDEAS-ERC Starting Grant Scheme, Project 278011 STUCCOFIELDS.

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Christiansen, S.H., Licht, M.W. Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms. Bit Numer Math 60, 345–371 (2020). https://doi.org/10.1007/s10543-019-00784-1

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