In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$ polynomials, where $r=0$ and $s$ is either $0$ or $1$. The discrete obstacle constraints are specifically applied to the cell unknowns. The analysis hinges on the construction of a suitable Lagrange multiplier, a residual functional and a linear averaging map. The reliability and the efficiency of the proposed a posteriori error estimator is discussed, and the study is concluded by numerical experiments supporting the theoretical results.

翻译：本文采用混合高阶方法讨论椭圆障碍问题的后验误差分析。该方法涉及用$r$次多项式表示的单元未知量和用$s$次多项式表示的边界未知量，其中$r=0$，$s$为$0$或$1$。障碍约束条件专门应用于单元未知量。分析基于构造合适的拉格朗日乘子、残差泛函和线性平均映射。讨论了所提出的后验误差估计子的可靠性与有效性，并通过数值实验验证了理论结果。