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Canonical construction of finite elements.(English)Zbl 0938.65132

This paper is devoted to the construction of conforming finite elements for spaces arising from vector analytic differential operators in arbitrary dimension. The differential forms and their features are a key instrument for a unified approach of finite element spaces. A simple characterization of the local polynomial spaces and degrees of freedom underlying the definition of the finite element spaces is given. The usual \({\mathbf H}(\text{Div};\Omega)\)- and \({\mathbf H}(\text{curl};\Omega)\)-conforming finite elements are recovered together with the unisolvence of degrees of freedom. Crucial algebraic properties of the canonical interpolation operators and representation theorems in a single sweep for all kinds of spaces are also obtained.
Reviewer: V.Arnăutu (Iaşi)

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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