A new viewpoint on mixed elements

Mixed elements are special finite elements for vector fields, whose shape functions are not necessarily continuous in all their components. They are used in connection with ‘two-field’ formulations, for instance when one tries simultaneously to compute displacement and stress in elasticity. We present here a family of finite elements which originate from a chapter of differential geometry apparently unconnected with numerical analysis (Whitney forms) and insist on the structural properties of this family considered as a whole. This sheds a new light on mixed elements, under which they acquire a more natural character than in previous presentations.SommarioGli elementi misti sono elementi finiti speciali per campi vettoriali le cui funzioni di interpolazione non sono necessariamente continue in tutte le componenti; tali elementi vengono usati nell'ambito delle formulazioni ‘a due campi’, per esempio quando si calcolano simultaneamente spostamento e tensione in elasticità. In questo articolo viene presentata una famiglia di elementi finiti che traggono origine da un costrutto di geometria differenziale che in apparenza non ha alcun nesso con l'analisi numerica (le forme di Whitney): vengono illustrate le proprietà strutturali complessive di tale famiglia. Questa presentazione getta una nuova luce sugli elementi misti, sotto la quale essi acquistano un carattere più naturale.

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