ABSTRACT
This chapter presents only a few one- and two-dimensional elements, chosen among those used in the analysis of heat transfer and related fluid flow problems. It discusses finite element discretizations in space with reference to suitable interpolating functions defined in terms of local coordinates. The chapter suggests that finite element discretizations in the space dimensions can be used in the analysis of unsteady problems to obtain matrix differential equations that are only partially discretized. It discusses the element behaviors in terms of nodal values and offers the final systems of algebraic equations. In the general context of finite element methods, stability constraints can be easily determined analytically only for one-dimensional domains subdivided into linear elements of uniform size. In addition to discretization errors, any computer solution leads to roundoff errors stemming from the finite number of significant figures in the machine representation of variables.
