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

## TL;DR

This paper introduces an active-set mixed finite element method for simulating cavitation in hydrodynamic lubrication, providing a robust numerical approach with proven existence and efficient solution strategies.

## Contribution

It develops a novel active-set mixed finite element solver tailored for transient cavitation problems in hydrodynamic lubrication, combining a characteristics method with a weak formulation.

## Key findings

- Proved unique solvability of the discretized problem.
- Developed an efficient primal-dual active-set algorithm.
- Demonstrated the method's effectiveness through numerical examples.

## Abstract

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.