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.

中文翻译：

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Signorini问题的合规模型误差分析

本论文涉及一类受惩罚的 Signorini 问题，也称为正常合规模型。这些非线性模型近似于 Signorini 问题，并以惩罚参数\(\varepsilon \)和“功率参数” \(\alpha \ge 1\) 为特征，其中\(\alpha = 1\)对应于标准处罚。我们在空间维度\(d=2,3\) 中选择了一个连续符合线性有限元近似，并在讨论和分析的各种假设下获得\(L^2\)误差估计。