On the convergence of a mixed finite element scheme for plate bending

The convergence of a mixed finite element scheme for plate bending, previously proposed by the present authors, is discussed on the basis of functional analysis. First, the outline of the formulation is presented with some mathematical preliminaries. Then, several kinds of energy inequalities are established to assure the stability of the approximate solution. Thus, the rate of convergence may be obtained by the evaluation of the degrees of the completeness and consistency of the employed shape functions. Some remarks are also given with respect to the extension of the method to initial value problems.