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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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 (2019). https://doi.org/10.1007/s10543-019-00784-1
- Discrete distributional differential form
- Finite element exterior calculus
- Finite element method
- Homology theory
- Poincaré–Friedrichs inequality
Mathematics Subject Classification