TITLE:

Discrete compactness and Fortin operator for edge elements

Author(s): Daniele Boffi
Status: Numer. Math., submitted
Report #: AM187

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Abstract:

The basic properties of the edge elements are proven in the original papers by Nédélec. In the two-dimensional case the edge elements are isomorphic to the face elements (the well-known Raviart--Thomas elements), 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. 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.

URL(s): http://dimat.unipv.it/~boffi    

Email(s): boffi@math.psu.edu