Istituto di Matematica Applicata e Tecnologie Informatiche     
Bathe K., Brezzi F. Stability of Finite Element Mixed Interpolations for Contact Problems. Preprint ercim.cnr.ian//2001-1219, 2001.
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.
Subject Contact problems, Elasticity, inf-sup condition
65N30, 65N15, 65N50

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