Variational inequality for the free boundary problem

Abstract

We study a free boundary problem arising from a unidirectional gravity-driven steady flow. Under certain geometrical assumptions, the free boundary problem is equivalent to a variational inequality. In this thesis we used the damped Newton method to solve the finite dimensional variational inequality problem obtained by finite element method. The damped Newton method in itself has the locally quadratic convergence. Numerical results are presented to determine the free boundary and to confirm the theoretical estimates predicted by theory.