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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
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     author = {Bathe, Klaus J\"urgen and Brezzi, Franco},
     title = {Stability of finite element mixed interpolations for contact problems},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {167--183},
     year = {2001},
     volume = {Ser. 9, 12},
     number = {3},
     zbl = {1097.74054},
     mrnumber = {MR1898458},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_3_a2/}
}
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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/