Historical corner column: A prelude to finite elements: The fruitful problem of the brachistochrone

Abstract

When did finite elements begin? It is difficult to trace the origins of finite-element methods because of a basic problem in defining precisely what constitutes a “finite-element method.” To most mathematicians, it is a method of piecewise polynomial approximation. Its origins are therefore frequently traced to the appendix of a paper by Courant [1], in which piecewise-linear approximations of the Dirichlet problem over a network of triangles was discussed. The “Interpretation of Finite Differences” by Polya [2] is regarded as embodying piecewise-polynomial approximation aspects of finite elements.