A partition of unity method for a class of fourth order elliptic variational inequalities

We consider a partition of unity method (PUM) for a class of fourth order elliptic variational inequalities on convex polygonal domains that include obstacle problems of simply supported Kirchhoff plates and elliptic distributed optimal control problems with pointwise state constraints as special cases. By including singular functions in the local approximation spaces we are able to show that the partition of unity method converges optimally. Numerical results that corroborate the theoretical estimates are also presented.