New method about adaptive finite element algorithm for solving obstacle problems

The obstacle problem, which can be regard as a free boundary problem, is a typical of variational inequalities of the first kind. In this paper the domain is divided into three parts: linear elliptic partial differential equation area, entire contact area and free boundary area. We adopt different estimate strategies for different parts to propose a new adaptive finite element algorithm for obstacle problem. Numerical experiments approve of optimal convergence order obtained by the algorithm.