  We show quasi-optimality and a posteriori error estimates for the
frictionless contact problem between two elastic bodies with a zero-gap
function. The analysis is based on interpreting Nitsche's method as a
stabilised finite element method for which the error estimates can be obtained
with minimal regularity assumptions and without the saturation assumption. We
present three different Nitsche's mortaring techniques for the contact boundary
each corresponding to a different stabilising term. Our numerical experiments
show the robustness of Nitsche's method and corroborates the efficiency of the
a posteriori error estimators.

Numerical Analysis;Numerical Analysis