  In this paper we study a moving free boundary problem related to the the
cavitation modeling in lubricated devices. More precisely, a characteristics
method combined with a weak formulation in a mixed form is introduced for the
Elrod-Adams model. The formulation is suitable for the use of mixed finite
element methods in the numerical approximation. It is proved that the
time-discrete problem and its finite element discretization has a unique
solution. Further an efficient primal-dual active-set strategy is proposed to
solve the resulting algebraic system. The performance of the overall algorithm
is illustrated by numerical examples.
