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01-09-2021 | Issue 3/2021

# Error analysis of the compliance model for the Signorini problem

Journal:
Calcolo > Issue 3/2021
Authors:
Pierre Cantin, Patrick Hild
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## Abstract

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.