NCP Function-Based Dual Weighted Residual Error Estimators for Signorini's Problem

In this paper, we onsider goal-oriented adaptive nite element methods for Signorini's problem. The basis is a mixed formulation, whi h is reformulated as nonlinear variational equality using a nonlinear omplementarity (NCP) fun tion. For a general dis retization, we derive error identities with respe t to a possible nonlinear quantity of interest in the displa ement as well as the onta t for es, whi h are in luded as Lagrange multiplier, using the dual weighted residual (DWR) method. Afterwards, a numeri al approximation of the error identities is introdu ed. We exemplify the results for a low order mixed dis retization of Signorini's problem. The theore ti al ndings and the numeri al approximation s heme are nally substantiated by some numeri al examples.