Error analysis of the compliance model for the Signorini problem
Résumé
The present paper is concerned with a class of penalized Signorini problems also called normal compliance models. These nonlinear models approximate the Signorini problem and are characterized both by a penalty parameter ε and by a "power pa-rameter" α ≥ 1, where α = 1 corresponds to the standard penalization. We choose a continuous conforming linear finite element approximation in space dimensions d = 2, 3 to obtain an L 2-error estimate of order h 2 when d = 2, α = 2, ε ≥ θh (θ large enough) and when the solution is W 2,3-regular. A similar estimate is obtained when d = 3 under slightly more restrictive assumptions on ε.
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