Fourth-order elliptic problems arise in a variety of applications from thin plates to phase separation to liquid crystals. A conforming Galerkin discretization requires a finite dimensional subspace of H2, which in turn means that conforming finite element subspaces are C1-continuous. In contrast to standard H1-conforming C0-elements, C1-elements, particularly those of high order, are less understood from a theoretical perspective and are not implemented in many existing finite element codes. In this talk, we address the implementation of the elements. In particular, we present algorithms that compute C1-finite element approximations to fourth-order elliptic problems and which only require elements with at most C0-continuity. The algorithms are suitable for use in almost all standard finite element packages. Iterative methods and preconditioners for the subproblems in the algorithm will also be presented.
