A new viewpoint on mixed elements
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.
scientific article; zbMATH DE number 95214
scientific article