Mixed Defect Correction Iteration for the Solution of a Singular Perturbation Problem

We describe a discretization method (mixed defect correction) for the solution of a two-dimensional elliptic singular perturbation problem. The method is an iterative process in which two basic discretization schemes are used: one with and one without artificial diffusion. The resulting method is stable and yields a 2nd order accurate approximation in the smooth parts of the solution, without using any special directional bias in the discretization. The method works well also for problems with interior or boundary layers.