  In this paper, we present and analyze a posteriori error estimates in the
energy norm of a quadratic finite element method for the frictionless
unilateral contact problem. The reliability and the efficiency of a posteriori
error estimator is discussed. The suitable decomposition of the discrete space
$\b{V^h}$ and a discrete space $\b{Q^h}$, where the discrete counterpart of the
contact force density is defined, play crucial role in deriving a posteriori
error estimates. Numerical results are presented exhibiting the reliability and
the efficiency of the proposed error estimator.
