A local error estimator using finite element residual and duality

A quasistatic frictional contact formulation is derived from a dynamic contact problem using time-discretized approximation, for which a compliant interface model of the contact surface is assumed. An a posteriori error estimator is developed by a Lagrangian formulation which is recast into a set of local problems with equilibrated normal stress. Hence, local errors are calculated by solving these local element-wise problems, and can be used to obtain optimal meshes through an adaptive hp-finite element method based on a priori and a posteriori error estimates. The theory is applied to representative test problems of frictional contact, and numerical simulation results are given to support the theoretical results.