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Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension

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Abstract

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. In particular we define regularization operators which, combined with the standard interpolators, enable us to prove discrete Poincaré–Friedrichs inequalities and discrete Rellich compactness for finite element spaces of differential forms of arbitrary degree on compact manifolds of arbitrary dimension.

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  1. CMA c/o Department of Mathematics, Universitetet i Oslo, P.O. Box 1053, Blindern, NO-0316, Oslo, Norway

    Snorre H. Christiansen

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Christiansen, S.H. Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension. Numer. Math. 107, 87–106 (2007). https://doi.org/10.1007/s00211-007-0081-2

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  • DOI: https://doi.org/10.1007/s00211-007-0081-2

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