In this article, we develop a posteriori error analysis of a non-conforming finite element method in the supremum norm for the elliptic obstacle problem. In the analysis, the proper construction of the discrete Lagrange multiplier helps in obtaining the desired sign property of its average over the elements. The sub- and super-solutions, Green’s function, residual functional, and averaging operator are used crucially in proving the reliability of the proposed error estimator. Numerical results validating the theoretical results and illustrating the reliability and the efficiency of the error estimator are presented.

中文翻译：

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障碍问题的逐点自适应非协调有限元法

在本文中，我们对椭圆障碍问题的最高范数中的非相容有限元方法进行了后验误差分析。在分析中，离散拉格朗日乘子的正确构造有助于获得元素平均值的所需符号属性。子解和超解、格林函数、残差函数和平均算子在证明所提出的误差估计器的可靠性方面至关重要。数值结果验证了理论结果并说明了误差估计器的可靠性和效率。