A Brief History of the Beginning of the Finite Element Method

The purpose of this paper is to trace the development of the ideas which led to the method of analysis in which the field equations of mathematical physics are approximated over simple regions (triangles, quadrilaterals, tetrahedrons, etc.), and then assembled together so that equilibrium o r continuity is satisfied at the interconnecting nodal points of the domains. The technique thus realized is now referred to as the finite element method (FEM). It is natural to assume that if the size of the approximating domains becomes infinitely small, the solutions so obtained tending to this limit by successive mesh refinement converge towards the analytic solution. It is also noted that the subdivision should in addition reproduce the constant function space (e.g. strain, curvature, potential), since the representation of this state must be independent of mesh size (i.e. a larger mesh is obtained from a smaller one by simple magnification, but the function field remains constant). There are five groups of papers which may be considered in the development of the FEM and in one of these the name originated. They are the papers by Courant,' Argyris,' Turner et ~ l . , ~ C l o ~ g h ~ ~ and Zienkiewicz.' The present paper examines the contribution of each of these five groups of papers and attempts to put them in their place in the history of the FEM. In this survey of the papers the motivation is to examine the contributions by the following criteria: