Adaptive quadratic finite element method for the unilateral contact problem

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 $\text{b}{V}^h$ and a discrete space $\text{b}{Q}^h$, 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.