Geodesic
Stability of finite element mixed interpolations for contact problems
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 3, pp. 167-183.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need for technicalities, the analysis of the finite element discretizations to solve the problem gives valuable insight and allows quite general conclusions on the use of different interpolation schemes.
Si considera il problema del contatto senza penetrazione di due corpi elastici, usando la tecnica dei moltiplicatori di Lagrange per il trattamento del vincolo unilaterale. La discretizzazione con elementi finiti di tale problema deve soddisfare opportune condizioni di stabilità, che includono una condizione di inf-sup. Per identificare la tipologia degli elementi finiti che possono portare a schemi discretizzati stabili (ed ottimali) ci concentriamo sulla discretizzazione di un problema modello «semplice». Tale scelta permette di evitare un certo numero di tecnicismi, pur fornendo valide indicazioni sulle scelte da operare in contesti molto più generali. 
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Bathe, Klaus Jürgen; Brezzi, Franco. Stability of finite element mixed interpolations for contact problems. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 3, pp. 167-183. http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_3_a2/

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