A Level Set Method for Solving Free Boundary Problems Associated with Obstacles

Abstract

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two different approaches are described and applied for solving a unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: firstly, a proximal bundle method, which is a method for solving general nonsmooth optimization problems. Secondly, a gradient method is proposed for solving the regularized problems. Numerical experiments are included to verify the convergence of the methods and the quality of the results.