Fortin operator and discrete compactness for edge elements

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Abstract

The basic properties of the edge elements are proven in the original papers by Nédélec [22,23]. In the two-dimensional case the edge elements are isomorphic to the face elements (the well-known Raviart-Thomas elements [24]), so that all known results concerning face elements can be easily formulated for edge elements. In three-dimensional domains this is not the case. The aim of the present paper is to show how to construct a Fortin operator which converges uniformly to the identity in the spirit of [5,4]. The construction is given for any order tetrahedral edge elements in general geometries. We relate this result to the well-known commuting diagram property and apply it to improve the error estimate for a mixed problem which involves edge elements. Finally we show that this result can be applied to the analysis of the approximation of the time-harmonic Maxwell's system.
Original languageEnglish (US)
Pages (from-to)229-246
Number of pages18
JournalNumerische Mathematik
Volume87
Issue number2
DOIs
StatePublished - Jan 1 2000
Externally publishedYes

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