A Penalization Method for the Elliptic Obstacle Problem

Cornel Murea* and Dan Tiba

In this paper we propose a new algorithm for the wellknown elliptic obstacle problem. Our approach enters the category of fixed domain methods and solves just linear elliptic equations at each iteration. The approximating coincidence set is explicitly computed and it converges in the Hausdorff-Pompeiu sense to the searched geometry. In the numerical examples, the algorithm has a very fast convergence.

Mathematics Subject Classification: 35R35 35J86

Keywords: obstacle problem; free boundary problems; penalization;

Minisymposion: Shape Optimization and Free Boundaries