The Finite Element Methods Of Two Kinds Of Variational Inequalities

In this paper we first apply the quadratic conforming finite element to the second order variational inequality with displacement obstacle in smooth domain. Based on the newinterpolation skills, we get the same error order O(h3/2 )in the convex domain with smooth boundary as in the convex polygon one.Then, for the fourth order curvature obstacle problem, by using modified the approximate formulation and using the novel tricks, we discuss the nonconforming Morley's finite element approximation and get a new error estimation .Finally, we discuss the other two new nonconforming rectangular elements approximations to the fourth order obstacle problem. It is shown that the conclusions obtained above are still valid.