Use of the least squares criterion in the finite element formulation

This paper presents a new method of formulating the finite element relationships based on the least squares criterion. To overcome the high degree of inter-element continuity, a method of reducing the original governing differential equation to a set of equivalent system of first-order differential equations is proposed. The validity of the method is demonstrated by means of several numerical examples. In particular, application of the method to problems with unknown variational functionals is considered.