ABSTRACT
Building on our discussion of the finite element method for the one-dimensional steady diffusion equation in Chapter 1, we proceed to illustrate the implementation of the method to other ordinary and partial differential equations in one spatial dimension. We begin by discussing procedures for advancing in time the solution of the unsteady diffusion equation and the convection equation, and then study the solution of the convection-diffusion equation at steady state. In Sections 2.4-2.6, we consider applications in structural mechanics with reference to the bending and buckling of beams, governed by fourth-order differential equations. The union of the problems considered in this chapter provides us with an extended methodology that can be used with straightforward adaptations to solve general ordinary and partial differential equations.
