A posteriori error analysis of hybrid high-order methods for the elliptic obstacle problem (Q6645944)

In this article, a posteriori error analysis of hybrid high-order (HHO) methods is studied for the elliptic obstacle problem. The HHO method involves cell unknowns represented by degree-\(r\) polynomials with \(r = 0\) and face unknowns represented by degree-\(s\) polynomials, either \(0\) or \(1\). The imposition of discrete obstacle constraints targets the cell unknowns. The error analysis relies upon the construction of a discrete Lagrange multiplier, a residual functional and a linear averaging operator which maps the functions from the discontinuous finite element space to the conforming finite element space. The reliability of the proposed error estimator in the energy norm is established and the efficiency of the error estimator is demonstrated. Numerical results in two dimension validate the theoretical performance of the a posteriori error estimator.