ABSTRACT
This chapter makes an extensive use of the finite element method to solve complex, continuous problems for which no analytical solutions are available. It discusses the way to the presentation of a general discretization procedure that can be used to generate the systems of algebraic equations which are commonly derived in the solution of conduction and convection problems. The chapter considers first the techniques allowing the replacement of continuous variables by their approximating functions. It also discusses the integral statements which can be applied to the approximate, discrete equivalents to obtain the final sets of simultaneous algebraic equations. The chapter describes several forms of these differential equations which have a bearing on practical applications. It introduces from basic principles, the subject of piece-wise approximation and the Galerkin weighted residual method. The chapter illustrates the space discretization of continuum problems through simple one-dimensional examples.
