A new numerical approach of a lubrication free boundary problem

Abstract

A combination of a semidiscretized scheme and an iterative method is applied to a free boundary problem. The considered problem is issued from a cavitation model in lubrication theory and treats on the determination of the cavitation area. Estimates L∞(Ω) which provide the convergence of the approximated solution is obtained. Finally, some numerical test examples are presented to illustrate the good performance of the method.