ABSTRACT
In the preceding chapter, the basic concepts of numerical methods were presented as solutions to real physical problems. These methods are used to solve problems of practical significance which do not possess derivable or accurate closed-form solutions. Such numerical methods provide an approximation to the governing equations in terms of values at a finite number of discrete points within the computational domain. The current practice is reflected by the assertion of Irons and Shrive (1983): ‘if there is an opportunity for improving the design, then somebody is attempting to do so using the finite element method’. However, to meet such expectations, it is also essential that numerical errors can be quantified so that solutions of engineering projects especially where life safety must be ensured (such as bridges), meet certain permissible accuracy standards.
