Dual Weighted Residual Error Control for Frictional Contact Problems

Abstract In this paper goal-oriented error control based on the dual weighted residual error method (DWR) is applied to frictional contact problems. The derivation of DWR error controls is done for arbitrary discretization schemes via the introduction of some discrete Lagrange multipliers describing the residual of the discretization. The discrete Lagrange multipliers may be provided by a reconstruction in a post-processing step or by a discretization of a mixed formulation in which they are directly available. The error controls are defined for user-defined functionals (the quantities of interest) which measure the error of the displacement field as well as the normal and tangential contact forces. Numerical experiments confirm the applicability of the estimates within adaptive schemes.