Numerical analysis of a contact problem with wear

Abstract

This paper represents a sequel to [13] where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in [13]. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.Keywords. Quasistatic contact problem, variational inequality, numerical methods, optimal order error estimate.

Error bound analysis of the D-gap functions for a class of elliptic variational inequalities with applications to frictional contact mechanics

“…Then, we revisit the following classical formulation of the contact problem without wear which is a special case of problems considered in [13,41].…”