Elements and Shape Functions

Domain discretization is one of the most important steps in many numerical methods to solve boundary value problems. In finite element method (FEM), the whole domain is discretized by elements. In boundary element method (BEM) the boundary of the domain is discretized by elements. The choice of the geometry of the element and the form of the approximating function to represent the behaviour of field variables (such as the potential φ, field strength E H and so on) within each element are both extremely important. They strongly influence the accuracy of the results, the computing time and the software engineering of computer programs. Hence the problem of element discretization is a generic problem and is common to element approximate methods as well as FEM. Hence element discretization techniques are discussed in one chapter.