Theory and examples of partial approximation in the finite element method

This paper presents theory and examples of partial approximation as a modification of the displacement method in the finite element analysis. This method requires different shape functions for different terms in the potential energy expression to curtail the processes in the standard displacement method. Explanation of the theory is given by use of a simple example for Poisson's equation. It can also be effectively utilized to give mathematical foundation to some finite element models based on physical reasonings, such as Melosh's rectangular element for plate bending and beam element approximation of circular arches.