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01-09-2021 | Issue 3/2021

Calcolo 3/2021

Error analysis of the compliance model for the Signorini problem

Calcolo > Issue 3/2021
Pierre Cantin, Patrick Hild
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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 \(\varepsilon \) and by a “power parameter” \(\alpha \ge 1\), where \(\alpha = 1\) corresponds to the standard penalization. We choose a continuous conforming linear finite element approximation in space dimensions \(d=2,3\) and obtain \(L^2\)-error estimates under various assumptions which are discussed and analyzed.

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