A FEM FOR A SYSTEM OF SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS SOURCE TERM

In this paper, we consider a weakly coupled system of two reaction-diffusion equations with discontinuous source terms. When a parameter multiplying the second order derivatives in the equations is small, their solutions exhibit boundary layers as well as interior layers. A numerical method based on finite element and Shishkin and Bakhvalov–Shishkin meshes is presented. We derive an error estimate of order O(N-1ln N) in the energy norm with respect to the perturbation parameter. Numerical experiments are also presented to support our theoritical results.