TABLE OF CONTENTS In Secs 2.2 and 2.3 we presented several currently used procedures for dealing with the steady-state convection-diffusion equation with a scalar variable. All of these translate essentially to the use of streamline Petrov-Galerkin discretization, though of course the modification of the basic equations to a self-adjoint form given in Sec. 2.2.4 provides the full justification of the special weighting. Which of the procedures is best used in practice is largely a matter of taste, as all can give excellent results.
The generalized representation of all the stabilization methods discussed in this part may be written as
where ? i is a stabilizing parameter.
In the second part of this chapter dealing with transient problems it will be found that similar stabilizing forms arise directly when steady state is reached or assumed.
In this case the parameter ? i is now replaced by another one involving the length of the time step ? t. We shall show at the end of the next section a comparison between various procedures for stabilization and will note essentially the same forms in the steady-state situation.
