  Discontinuous Galerkin (DG) methods are considered for solving a plate
contact problem, which is a 4th-order elliptic variational inequality of second
kind. Numerous $C^0$ DG schemes for the Kirchhoff plate bending problem are
extended to the variational inequality. Properties of the DG methods, such as
consistency and stability, are studied, and optimal order error estimates are
derived. A numerical example is presented to show the performance of the DG
methods; the numerical convergence orders confirm the theoretical prediction.
