SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1687-1712, August 2024.
Abstract. In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in [math], for [math] in two spatial dimensions. This new analysis treats the positive and negative parts of the discretization error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in [math] for any [math]. We summarize extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory.

中文翻译：

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Signorini 问题的基于对偶的误差控制


《SIAM 数值分析杂志》，第 62 卷，第 4 期，第 1687-1712 页，2024 年 8 月。

抽象的。在本文中，我们研究 Signorini 问题的一致分段线性有限元近似的后验界限。我们证明了[数学]中残差类型的新严格后验估计，对于二维空间中的[数学]。这种新的分析分别处理离散化误差的正数和负数部分，需要一种新颖的符号和边界保留插值，该插值被证明具有最佳逼近属性。这些估计依赖于任何[数学]的[数学]问题的尖锐双稳定性结果。我们总结了广泛的数值实验，旨在测试估计器的稳健性以验证该理论。