The recently proposed expanded mixed formulation for numerical solution of second order elliptic problems is here extended to fourth order elliptic problems. This expanded formulation for the differential problems under consideration differs from the classical formulation in that three variables are treated, i.e., the displacement and the stress and moment tensors. It works for the case where the coefficient of the differential equations is small and does not need to be inverted, or for the case in which the stress tensor of the equations does not need to be symmetric. Based on this new formulation, various mixed finite elements for fourth order problems are considered; error estimates of quasi-optimal or optimal order depending upon the mixed elements are derived. Implementation techniques for solving the linear system arising from these expanded mixed methods are discussed, and numerical results are presented.
This paper will appear in Numerical Methods for PDE.