Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms

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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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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Keywords

  • Discrete distributional differential form
  • Finite element exterior calculus
  • Finite element method
  • Homology theory
  • Poincaré–Friedrichs inequality

Mathematics Subject Classification

  • 65N30