  We consider the reaction diffusion problem and present efficient ways to
discretize and precondition in the singular perturbed case when the reaction
term dominates the equation. Using the concepts of optimal test norm and saddle
point reformulation, we provide efficient discretization processes for uniform
and non-uniform meshes. We present a preconditioning strategy that works for a
large range of the perturbation parameter. Numerical examples to illustrate the
efficiency of the method are included for a problem on the unit square.
