Finite element methods for the displacement obstacle problem of clamped plates

We study finite element methods for the displacement obstacle problem of clamped Kirchhoff plates. A unified convergence analysis is provided for C1 finite element methods, classical nonconforming finite element methods and C0 interior penalty methods. Under the condition that the obstacles are sufficiently smooth and that they are separated from each other and the zero displacement boundary constraint, we prove that the convergence in the energy norm is O(h) for convex domains.