An active-set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

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.