A finite element analysis of a coupled system of singularly perturbed reaction–diffusion equations

Abstract

We consider a system of two coupled reaction–diffusion equations. When the parameters multiplying the second-order derivatives in the equations are small, their solutions exhibit boundary layers. Moreover, when the parameters are of different magnitudes, two distinct but overlapping boundary layers are present. We study a finite element discretization on general layer-adapted meshes including the frequently studied Shishkin mesh and the Bakhvalov mesh. Supporting numerical results are presented.