Estimating error bounds for differential systems involving coupled variational-hemivariational inequalities with applications to quasistatic contact problems

The main goal of this study is to explore new error bounds for a complex class of differential nonlinear systems involving coupled variational-hemivariational inequalities with the nesting structure. We first construct suitable regularized gap functions of the corresponding control system consisting of coupled variational-hemivariational inequalities, and provide their relevant properties. Then, new error bounds for this class of differential nonlinear system are established based on the computational technologies involving coupled gap functions. Consequently, a result of error bounds for the history-dependent problem derived by coupled variational-hemivariational inequalities is also derived. Lastly, we apply the obtained error bound results to the quasistatic contact problems of two elastic bodies.