In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator.

翻译：本文针对Signorini问题，发展了一种基于残差的新型逐点后验误差估计器用于二次有限元方法。上确界范数后验误差估计使我们能够局部定位奇异性以控制逐点误差。在分析中，我们适当构造了接触力密度的离散对应量以展现所需的符号性质。我们利用散度型算子标准格林矩阵的先验估计，并通过适当修正离散解引入上下障碍函数。最后，数值实验展示了所提误差估计器的优异性能。