On mixed methods for fourth-order problems

A mixed finite element method for the problem v + σ²Δ²v = x with different types of boundary conditions is described. The method converges, and it is well suited for the analysis of various evolution problems. The computation of the discrete solution is made by applying a sequence of iterative methods for block matrices: correspondingly to each iteration either a couple of Poisson problems or a couple of problems for the identity operator are solved, according to the value of the parameter σ. Some numerical results for two model examples are presented.