Numerical Analysis of a Contact Problem with Wear
Provides rigorous error analysis for a specific contact problem with wear, incremental to prior work.
This paper extends previous work on numerical solutions for quasistatic contact problems with wear, deriving optimal order error bounds for a fully discrete scheme and confirming them with simulations.
This paper represents a sequel to the previous one, 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 the previous paper. 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.