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

Abstract

In this paper, we consider goal-oriented adaptive finite element methods for Signorini's problem. The basis is a mixed formulation, which is reformulated as nonlinear variational equality using a nonlinear complementarity function. For a general discretization, we derive error identities w.r.t. a possible nonlinear quantity of interest in the displacement as well as in the contact forces, which are included as Lagrange multiplier, using the dual weighted residual method. Afterwards, a numerical approximation of the error identities is introduced. We exemplify the results for a low order mixed discretization of Signorini's problem. The theorectical findings and the numerical approximation scheme are finally substantiated by some numerical examples.