# A Duality-Type Method for the Obstacle Problem

Diana Merlusca^{*}

We consider the obstacle problem in Sobolev spaces, of order strictly greater then the dimension of the domain. We have considered a new type of approximate problem and with the help of the duality we reduce it to a finite dimensional optimization problem and we prove convergence.\newline By analyzing the dual approximate problem we show that its solution is a linear combination of Dirac distributions. Taking into account this form of the solution, we are able to treat the approximate obstacle problem by simply solving a quadratic minimization problem and applying a formula which transfers the result back to the primal approximate problem.\newline We apply this algorithm successfully to some numerical examples.

Mathematics Subject Classification: 65K10 49M27

Keywords: obstacle problem, dual problem

Minisymposion: Shape Optimization and Free Boundaries