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.

翻译：我们考虑了反应扩散问题,提出了在单一扰动的情况下,在反应术语主导方程式时,在单一扰动的情况下,以有效的方式将反应扩散和先决条件分开。我们利用最佳试验规范概念和重新组合马鞍点的概念,为统一和非统一的模类提供了高效的分离过程。我们提出了一个用于大量扰动参数的前提条件战略。在单位方形出现问题时,包括了说明该方法效率的数字示例。