Volume 18, Number 2, Summer 2010
ANALYSIS AND NUMERICAL
APPROXIMATION OF A FRICTIONAL
UNILATERAL CONTACT PROBLEM WITH
Abstract. We consider a static contact problem between
a linear elastic body and an obstacle, the so-called foundation.
The contact is frictional and is modelled with a normal
compliance condition such that the penetration is restricted with
unilateral constraint, and the associated version of Coulomb's
law of dry friction. We derive a variational formulation and
prove its unique weak solvability if the friction coefficient is
sufficiently small. Moreover, we prove the continuous
dependence of the solution on the contact conditions. Also we study
the finite element approximation of the problem and obtain an
error estimate. Finally, we introduce an iterative method to
solve the discrete problem.