Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: The primal–dual formulation and a posteriori error estimation

We present an a priori analysis of the hp-version of the finite element method for the primal–dual formulation of frictional contact in linear elasticity. We employ a novel hp-mortar projection operator that is uniformly stable in the mesh width and grows slowly in the polynomial degree. We derive an hp-FEM residual error indicator, develop an hp-adaptive strategy that is based on testing for analyticity, and show in numerical examples that the adaptive algorithm can lead to exponential rates of convergence.