ABSTRACT
The finite element method (FEM) has developed along two paths. From the mathematical point of view, it is a method of constructing a function that makes the potential energy a minimum. From the engineering point of view, it is a method of assembling structural elements, which can be separately analyzed, into a global equation of equilibrium for the structure. The mathematical point of view makes the FEM a special form of the Rayleigh-Ritz method, which has a long history. The modern FEM may be said to have begun with Courant in 1943.1 His paper had little impact because the method was not practical until the development of digital computers in the 1950s. This approach has now been extensively explored by mathematicians and placed on a sound mathematical basis. Precise studies of error analysis and convergence proofs are available.2-5 However, the study of the mathematical foundations, involving Sobolev spaces, is beyond the scope of this book.
