1.7 Conclusion

In this first section of the book, we have introduced the concept of numerical approximations using the finite element method. We started with the simplest one-dimensional, linear, steady-state conduction problem, expanded the method to two- and three-dimensional elements, and ended with the time-dependent, nonlinear incompressible and compressible Navier Stokes and energy equations. Once the basic concepts are understood, the method can be readily applied to fluid dynamics, heat transfer, wave propagation, structural analysis, species transport, as well as a multitude of other transport related processes. Hopefully you now have an appreciation of the power and versatility of the finite element technique. You are now ready to move to the next section of this book that deals with the Boundary Element Method (BEM).