J. R. Fern\'ande, M. Shillor and M. Sofonea

Abstract. Numerical analysis and simulations are provided for a problem of
wear of an elastic beam that is in frictional contact with a moving
foundation. The process is assumed to be quasistatic, the contact is
modelled with normal compliance, and the wear is described by the
Archard law. Semi-discrete and fully discrete schemes for numerical
approximations of the problem are proposed, their unique solvability
established, and error estimates derived. Numerical simulations which
show the effective performance of the fully discrete algorithm are
presented.