A new viewpoint on mixed elements
type: Item
instance of: scholarly article
title: A new viewpoint on mixed elements
zbMATH Open document ID: 0778.65078
DOI: 10.1007/BF00452998
author: Alain Bossavit
published in: Meccanica
publication date: 1993-01-16T00:00:00Z
review text: The author presents a novel viewpoint in the interpretation of mixed finite elements. A relationship between the diagrams proposed by \textit{E. Tonti} [On the mathematical structure of a large class of physical theories, Rend. Acc. Lincei 52, 48-56 (1972)], the forms introduced by \textit{H. Whitney} [Geometric integration theory, Princeton Univ. Press, Princeton (1957; Zbl 0083.282)] and mixed finite elements is presented. As a consequence of this viewpoint, a class of so-called ``Whitney elements'' is introduced. These elements fall into a hierarchy of spaces whose degrees of freedom are variously associated with the nodes, edges, faces, and volumes of a tetrahedral tessellation. These elements are naturally well-suited to the same analyses generally performed using mixed finite elements. The Ladyzhenskaya-Babuška-Brezzi condition is immediately satisfied. Convergence of approximations using these non- conforming elements is a consequence of otherwise well-known theorems.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 95214
zbMATH Keywords: Tonti diagrams
zbMATH Keywords: Whitney elements
zbMATH Keywords: convergence
zbMATH Keywords: Whitney forms
zbMATH Keywords: complementarity
zbMATH Keywords: duality
zbMATH Keywords: mixed finite elements
zbMATH Keywords: non-conforming elements
reviewed by: Myron Sussman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 95214