Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem

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