The principle of subdomain methods has been introduced many years ago1
and such methods have been used with success in recent years. In this
paper, we discuss some methods used to solve the condensed system res
ulting from the Schur complement method. We will present the hybrid me
thod and a mechanical application: the contact problem between two def
ormable solids. In the case of such a problem, we propose two methods:
one for the contact with friction and one for the contact without fri
ction. Finally, the results of validation tests for both proposed appr
oaches are given.