A Posteriori Error Analysis of Hybrid High-Order Methods for the Elliptic Obstacle Problem

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 \(r=0\) $r=0$ 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.