Fortin operator and discrete compactness for edge elements |
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Authors: | Daniele Boffi |
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Institution: | (1) Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy; e-mail: boffi@dimat.unipv.it, IT;(2) Department of Mathematics, Penn State University, 218 McAllister Building, University Park, PA 16802, USA, US |
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Abstract: | Summary. 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.
Received March 22, 1999 / Revised version received September 23, 1999 / Published online July 12, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 65N30 65N25 |
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