A numerical study on the finite element solution of singularly perturbed systems of reaction–diffusion problems

We consider the approximation of singularly perturbed systems of reaction–diffusion problems, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. In this article we conduct a numerical study of several finite element methods applied to a model problem, having as our goal their assessment and the identification of a high order scheme which approximates the solution at an exponential rate of convergence, independently of the singular perturbation parameters.