International Journal of C 2004 Institute for Scientific Numerical Analysis and Modeling Computing and Information a Level Set Method for Solving Free Boundary Problems Associated with Obstacles

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two di erent approaches are described and applied for solving an unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: rstly, 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.

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