Some mathematical aspects

From the mathematical point of view the finite element method may be thought of as a technique for choosing the ‘best’ approximation to a solution from among a particular type or class of functions. These are called the trial functions. The criterion for the choice lies mainly with the physical laws which describe the problem, which are usually expressed as differential equations. The form of a differential equation is not immediately suitable for the finite element method; rather the problem has to be reformulated as a variational principle. In this chapter, where the setting is elasticity, the relevant variational principle is that of minimising the energy of the structure.