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Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms

  • Snorre H. Christiansen
  • Martin W. LichtEmail author
Article
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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.

Keywords

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

Mathematics Subject Classification

65N30 
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Notes

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloBlindernNorway
  2. 2.UCSD Department of MathematicsLa JollaUSA

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