Upper and lower bounds on quantities of interest for contact problems

This paper is devoted to acquiring strict bounds on discretization error as well as quantities of interest for contact problems. On the one hand, there are two key steps in estimating the discretization error: the first is the proper construction of approximate contact forces and the second is the utilization of the strict upper bounding property inherent in the constitutive relation error (CRE). On the other hand, upper and lower bounds on quantities of interest are derived through an optimization procedure. Academic examples are performed to verify the proposed bounds.