Splines and Finite Elements

Abstract

The finite element method is the general method for the numerical solution of partial differential equations covering all three main types of equations, namely elliptic, parabolic and hyperbolic equations. The finite element method is also a general technique for numerical solution of differential and integral equation in science and engineering. The method was introduced by engineers in the late 50’s and early 60’s for the numerical solution of partial differential equations in structural engineering (elasticity equations, plate equations, etc.). At this point the method was thought as a generalization of earlier methods in structural engineering for beams, frames and plates, where the structure was subdivided into small parts, so called finite elements, with known simple behaviour.